Abstract: Disclosed herein is an organization of cache memory for hardware acceleration of the FDTD method. The organization of cache memory for hardware acceleration of the FDTD method provides a substantial speedup to the finite-difference time-domain (FDTD) algorithm when implemented in a piece of digital hardware. The organization of cache memory for hardware acceleration of the FDTD method utilizes a very high bandwidth dual-port on-chip memory in a particular way. By creating many small banks of internal memory and arranging them carefully, all data dependencies can be statically wired. This allows for a many-fold speedup over SRAM-based solutions and removes the burden of data dependence calculation that streaming SDRAM-based solutions must perform.

Abstract: The invention provides a method and apparatus for operations of addition, subtraction, multiplication, and division of fractions, decimals, percents, proportions and equations. It allows the students to find the transparent area models on their sheets with the correct parts shaded, (2) students can count the total number of parts and the total number of shaded parts in each model, (3) the relationship of the shaded parts to the total number in each model can be named, (4) by intersecting the vertical transparent area model for one whole with horizontal transparent area models for one whole to show examples of one whole being renamed several different ways.

Abstract: One embodiment of the present invention provides a system that solves an overdetermined system of interval linear equations. During operation, the system receives a representation of the overdetermined system of interval linear equations Ax=b, wherein A is a matrix with m rows corresponding to m equations, and n columns corresponding to n variables, and wherein x includes n variable components, b includes m scalar components, and m>n. Next, the system performs a Gaussian Elimination operation to transform Ax=b into the form [ T W ] ? x = [ u v ] , wherein T is a square upper triangular matrix of order n, u is a vector with n components, v is a vector with m?n components, and W is a matrix with m?n rows and n columns, wherein W is zero except in the last column, which is represented as a column vector z with m?n components. Next, the system performs an interval intersection operation based on the equations zixn=vi (i=1, . . . , m?n) and Tnnx=un to solve for xn.

Abstract: A method and system for solving a large system of dense linear equations using a system having a processing unit and one or more secondary processing units that can access a common memory for sharing data. A set of coefficients corresponding to a system of linear equations is received, and the coefficients, after being placed in matrix form, are divided into blocks and loaded into the common memory. Each of the processors is programmed to perform matrix operations on individual blocks to solve the linear equations. A table containing a list of the matrix operations is created in the common memory to keep track of the operations that have been performed and the operations that are still pending. SPUs determine whether tasks are pending, access the coefficients by accessing the common memory, perform the required tasks, and store the result back in the common memory for the result to be accessible by the PU and the other SPUs.

Abstract: One embodiment of the present invention provides a system for solving a system of equations in fixed-point form. During operation, the system receives a representation of the equations in fixed-point form and stores the representation a computer memory. Next, the system reduces the dimension of the system of equations, when possible, by eliminating variables in the system of equations to produce a reduced system of equations. The system then performs interval intersections based on the Fixed Point theorem to reduce the size of a box containing solutions to the reduced system of equations. In a variation on this embodiment, the system additionally applies interval techniques to find solutions to the system of equations, when such solutions exist.

Abstract: A method for obtaining a stable and accurate solution for an ill-conditioned system of normal equations associated with digital Weiner filter for a time invariant system and/or an autoregressive operator of an autoregressive model. A time invariant stochastic model, uses a Gram_Schmidt process of orthonormalisation to condition the coefficient matrix, a singular matrix associated with such a system of normal equations, to an identity matrix. The observed output of the digital Weiner filter and/or autoregressive operator is defined as a time advanced version of the input. The method has application in situations where digitized data at smaller sampling intervals are made available.

Abstract: In one embodiment, a system and method for solving linear programs includes a perceptron algorithm configured to move toward a solution to the linear program. A transform algorithm is configured to stretch portions of a vector space within which the linear program is defined. A decision module decides between continued application of the perceptron algorithm and application of the transform algorithm based on a rate at which the approximate solutions are approaching a satisfactory solution.

Abstract: An active set algorithm exploits a ‘hot start’ for the set of binding constraints at optimality along with efficient linear algebra to make rapid progress towards the solution. The linear algebra is designed to deal with degenerate constraints as the required factorizations are performed and as degeneracy emerges, and not via a mostly unnecessary pre-process step. Combined together, these novel approaches enable solution of the control problem in real-time.

Abstract: A method and apparatus for quantum computing. A computer-program source code, data, and unsubstantiated output variables are converted into a class of computable functions by a program compiler. The computable functions are encoded, and a continualization method is applied to the encoded functions to determine a first-order, time-dependent, differential equation. Variational calculus is employed to construct a Lagrangian whose minimum geodesic is the solution for the first-order, time-dependent, differential equation. The Lagrangian is converted into a quantum, canonical, Hamiltonian operator which is realized as an excitation field via an excitation generator. The excitation field is repeatedly applied to a quantum processor consisting of a lattice of polymer nodes to generate an intensity-versus-vibrational-frequency spectrum of the lattice nodes.

Abstract: One embodiment of the present invention provides a system that solves a global optimization problem specified by a function ƒ and a set of equality constraints q1(x)=0 (i=1, . . . , r), wherein ƒ is a scalar function of a vector x=(x1, x2, x3, . . . xn). During operation, the system receives a representation of the function ƒ and the set of equality constraints and stores the representation in a memory within a computer system. Next, the system and performs an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of equality constraints. Performing this interval global optimization process involves, applying term consistency to the set of equality constraints over a subbox X, and excluding portions of the subbox X that violate the set of equality constraints.

Abstract: One embodiment of the present invention provides a system that uses a block-partitioned technique to efficiently solve a system of linear equations. The system first receives a matrix that specifies the system of linear equations to be used in performing a time-based simulation. This matrix includes a static portion containing entries that remain fixed over multiple time steps in the time-based simulation, as well as a dynamic portion containing entries that change between time steps in the time-based simulation. Next, the system performs the time-based simulation, wherein performing the time-based simulation involves solving the system of linear equations for each time step in the time-based simulation. In solving the system of linear equations, the system factorizes the static portion of the matrix only once, and reuses the factorization of the static portion in performing an overall factorization of the matrix for each time step of the time-based simulation.

Abstract: A projected iterative descent method is used to resolve LCPs related to rigid body dynamics, such that animation of the rigid body dynamics on a display system occur in real-time.

Abstract: A method of identifying one or more regions of the domain of a function that do not contain solutions is described along with a related subdivision method. These methods may be employed in the context of branch and bound methods that use interval analysis to search for solutions of functions. The one or more regions of the function domain that do not contain solutions are identified using a cropping formula derived from one or more components (low order and high order) of a Taylor Form inclusion function. A Corner Taylor Form inclusion function is also described which might be used to identify the output range of a function.

Abstract: A static schedule is selected from a set of static schedules for an application dependent on the state of the application. A scheduling system stores a set of pre-defined static schedules for each state of the application. A scheduling system learns the costs of predefined schedules for each state of the application on-line as the application executes. Upon the detection of a state change in the application during run-time, the scheduling system selects a new static schedule for the application. The new static schedule is determined based on schedule costs and exploration criteria.

Abstract: A calculating apparatus comprises a memory and a calculating section. The memory is stored with table data for referencing a value of a variable x by using a value of a variable y and a value of a solution z. The calculating section inputs x_in and y_in, reads two values y_a and y_b corresponding to y_in from the memory, reads two values x_aa and x_ab corresponding to x_in from the memory in a line corresponding to y_a, reads two values x_ba and x_bb corresponding to x_in from the memory in a line corresponding to y_b, and calculates a solution z corresponding to x_in and y_in in an interpolation by using x_in and y_in and the read values y_a, y_b, x_aa, x_ab, x_ba, and x_bb.

Abstract: A computer method of vector operations for calculating the inverse of a general square matrix and for solving linear equations systems. The invention comprises a new method of factorization and executing multiply-add operations useful for effecting dot-product operations of one-dimensional vectors. This new method reduces the computation time over computers programmed to use prior art methods.

Abstract: A system that solves a global inequality constrained optimization problem specified by a function ƒ and a set of inequality constraints pi(x)?0(i=1, . . . , m), wherein ƒ and pi are scalar functions of a vector x=(x1, x2, x3, . . . xn). The system performs an interval inequality constrained global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of inequality constraints. The system applies term consistency and box consistency to a set of relations associated with the global inequality constrained optimization problem over a subbox X, and excludes any portion of the subbox X that violates the set of relations. The system also performs an interval Newton step on the subbox X to produce a resulting subbox Y. The system integrates the sub-parts of the process with branch tests designed to increase the overall speed of the process.

Abstract: One embodiment of the present invention provides a system that solves a global optimization problem specified by a function ƒ and a set of inequality constraints pi(x)?0 (i=1, . . . , m), wherein ƒ and pi are scalar functions of a vector x=(x1, x2, x3, . . . xn). The system operates by receiving a representation of the function ƒ and the set of inequality constraints, and then storing the representation in a memory within the computer system. Next, the system performs an interval inequality constrained global optimization process to compute guaranteed bounds on the minimum value of the function ƒ(x) subject to the set of inequality constraints. While performing the interval global optimization process, the system applies term consistency at various places in the process over a subbox X, and excludes any portion of the subbox X that violates term consistency.

Abstract: One embodiment of the present invention provides a system that bounds the solution set of a system of nonlinear equations specified by the set of linear equations Ax=b, wherein A is an interval matrix and b is an interval vector. During operation, the system preconditions the set of linear equations Ax=b by multiplying through by a matrix B to produce a preconditioned set of linear equations M0x=r, wherein M0=BA and r=Bb. Next, the system widens the matrix M0 to produce a widened matrix, M, wherein the midpoints of the elements of M form the identity matrix. Finally, the system uses M and r to compute the hull h of the system Mx=r, which bounds the solution set of the system M0x=r.

Abstract: One embodiment of the present invention provides a system that solves a problem involving an interval parameter p through an interval solution process. During operation, the system receives a representation of the problem, wherein the problem includes a number of variables x1, x2, x3, . . . xn and at least one interval parameter p. The system stores the representation in a computer memory, and then performs the interval solution process on the problem. During this interval solution process, the system splits the problem into sub-problems by splitting the interval parameter p into subintervals, and creating separate sub-problems for each subinterval. The system then performs the interval solution process on the sub-problems. By splitting the interval parameter p, the system can achieve a tighter bound on the solution set of the problem. The decision to split on any parameter p is made in exactly the same way it would be made if p were a variable of the problem.

Abstract: One embodiment of the present invention provides a system that solves a global optimization problem specified by a function ƒ and a set of equality constraints qi(x)=0 (i=1, . . . , r), wherein ƒ is a scalar function of a vector x=(x1, x2, x3, . . . xn). During operation, the system receives a representation of the function ƒ and the set of equality constraints and stores the representation in a memory. Next, the system performs an interval equality constrained global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) subject to the set of equality constraints. During this process, the system applies term consistency to a set of relations associated with the interval equality constrained global optimization problem over a subbox X, and excludes any portion of the subbox X that violates the set of relations. It also applies box consistency to the set of relations, and excludes any portion of the subbox X that violates the set of relations.

Abstract: A method and system for secure computational outsourcing and disguise. According to an embodiment, a first set of actual arguments and a second set of actual arguments for an outsourced computation are determined. A first group of disguised arguments corresponding to the first set of actual arguments is prepared with a first computer. A second group of disguised arguments corresponding to the second set of actual arguments is prepared with a second computer. The first and second groups of disguised arguments are output from the first and second computers, respectively, for performance of the outsourced computation. A third computer performs the outsourced computation and returns a disguised result to the first and/or second computers. The first and/or second computers then unveil the actual result from the disguised result.

Abstract: One embodiment of the present invention provides a system that performs a procedure to solve a system of linear inequalities. During operation, the system receives a representation of the system of linear inequalities Ax?b, wherein Ax?b can be a linearized form of a system of nonlinear equations. Within this representation, A is an interval matrix with m rows corresponding to m inequalities, and with n columns corresponding to n variables, the vector x includes n variable components, and the vector b includes m scalar interval components. The system solves the system of linear inequalities Ax?b by performing a Gaussian elimination process using only positive multipliers so as not to change the sense of any inequality.

Abstract: One embodiment of the present invention provides a system that receives a representation of the function ƒ and stores the representation in a memory. Next, the system performs an interval global optimization process to compute guaranteed bounds on a globally minimum value of the function ƒ(x) over a subbox X. This interval global optimization process applies term consistency to a set of relations associated with the function ƒ over the subbox X, and excludes any portion of the subbox X that violates any member of the set of relations. It also applies box consistency to the set of relations associated with the function ƒ over the subbox X, and excludes any portion of the subbox X that violates the set of relations.

Abstract: One embodiment of the present invention provides a system for finding the roots of a system of nonlinear equations within an interval vector X=(X1, . . . , Xn), wherein the system of non-linear equations is specified by a vector function ƒ=(ƒ1, . . . , ƒn). The system operates by receiving a representation of the interval vector X (which is also called a box), wherein for each dimension, i, the representation of Xi includes a first floating-point number, ?i, representing the left endpoint of Xi, and a second floating-point number, bi, representing the right endpoint of Xi. Next, the system performs an interval Newton step on X to produce a resulting interval vector, X?, wherein the point of expansion of the interval Newton step is a point, x, within the interval X, and wherein performing the interval Newton step involves evaluating ƒ(x) to produce an interval result ƒ1(x).

Abstract: A multiplicand is multiplied by a multiplier using a modulus. The multiplicand, the multiplier and the modulus are polynomials of variable. A multiplication look-ahead method to obtain a multiplication shift value is carried out. An intermediate result polynomial is shifted to the left by the number of digits of the multiplication shift value. A reduction shift value equalling the difference of the degree of the shifted intermediate result polynomial and the degree of the modulus polynomial is obtained in a reduction look-ahead method. The modulus polynomial is then shifted by a number of digits equalling the reduction shift value. In a three-operands addition, the shifted polynomial and the multiplicand are summed and the shifted modulus polynomial is subtracted. The modular multiplication are iteratively executed and processed progressively until all the powers of the multiplier polynomial have been processed.

Abstract: One embodiment of the present invention provides a computer-based system for solving a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents ƒ1(x)=0, ƒ2(x)=0, ƒ3(x)=0 . . . , ƒn(x)=0, wherein x is a vector (x1, X2, X3, . . . xn). The system operates by receiving a representation of a subbox X=(X1, X2, . . . , Xn), wherein for each dimension, i, the representation of Xi, includes a first floating-point number, ai, representing the left endpoint of Xi, and a second floating-point number, bi, representing the right endpoint of Xi. The system stores the representation in a computer memory. Next, the system applies term consistency to the set of nonlinear equations, ƒ1(x)=0, ƒ2(x)=0, ƒ3(x)=0, . . . , ƒn,(x)=0, over X, and excludes portions of X that violate the set of nonlinear equations. The system also applies box consistency to the set of nonlinear equations over X, and excludes portions of X that violate the set of nonlinear equations.

Abstract: One embodiment of the present invention provides a system for finding zeros of a function, ƒ, within an interval, X, using the interval version of Newton's method. The system operates by receiving a representation of the interval X. This representation including a first floating-point number, a, representing the left endpoint of X, and a second floating-point number, b, representing the right endpoint of X. Next, the system performs an interval Newton step on X, wherein the point of expansion is the midpoint, x, of the interval X. Note that performing the interval Newton step involves evaluating ƒ(x) to produce an interval result ƒI(x). If ƒI(x) contains zero, the system evaluates ƒ(a) to produce an interval result ƒI(a). It also evaluates ƒ(b) to produce an interval result ƒI(b).

Abstract: One embodiment of the present invention provides a system for finding the roots of a polynomial or a quadratic equation with interval coefficients. The system operates by receiving a representation of a polynomial equation, which can be a quadratic equation of the form F(x)=Ax2+Bx+C=0, wherein A=[AL, AU], B=[BL, BU] and C=[CL, CU] are interval coefficients. Next, the system computes intervals containing roots of the functions F1(x), F2(x), F3(x) and F4(x), wherein F1(x)=ALx2+BLx+CL, F2(x)=AUx2+BUx+CU, F3(x)=ALx2+BUx+CL and F4(x)=AUx2+BLx+CU. The system then places the computed intervals into a list, L, and orders the computed intervals in L by their left endpoints, so that for a each entry, Si=[SiL, SiU], SiL?Si+1,L. Next, the system establishes interval roots for F(x) from the interval entries in list L.

Abstract: A computer-based system for solving a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents ƒ1(x)=0, ƒ2(x)=0, ƒ3(x)=0, . . . , ƒn(x)=0, wherein x is a vector (x1, x2, x3, . . . xn). The system operates by receiving a representation of an interval vector X=(X1, X2, . . . , Xn), wherein for each dimension, i, the representation of Xi includes a first floating-point number, ai, representing the left endpoint of Xi, and a second floating-point number, bi, representing the right endpoint of Xi. For each nonlinear equation ƒi(x)=0 in the system of equations f(x)=0, each individual component function ƒi(x) can be written in the form ƒi(x)=g(x?j)?h(x) or g(x?j)=h(x), where g can be analytically inverted so that an explicit expression for x?j can be obtained: x?j=g?1(h(x)). Next, the system substitutes the interval vector element Xj into the modified equation to produce the equation g(X?j)=h(X), and solves for X?j=g?1(h(X)).

Abstract: A method of measuring temperature of a component capable of emitting thermal radiation and reflecting background radiation comprising the steps of: providing a pyrometer for measuring the radiation from the component, characterised by coating a part of the component with a first emissivity coating and a part of the component with a different and second emissivity coating, each with known emissivities EH and EL respectively, recording a first radiation measurement from the first emissivity coating RH and a second radiation measurement from the second emissivity coating RL, then calculating the true radiation RBlade from the component from the equation 1 R Blade = ( R H E H - R L E H ⁢ ( 1 - E H 1 - E L ) ) ( 1 - E L E H ⁢ ( 1 - E H 1 - E L ) )

Abstract: In a simultaneous-linear-equations solving method of calculating the numerical solutions of simultaneous linear equations having a coefficient matrix, all the elements of coefficient matrix elements including zero elements and all the elements of right-side vector elements are stored into an array. Next, a non-zero-structure-specifying index table is created which indicates the row number of a terminal-end non-zero element in each column and the column number of a terminal-end non-zero element in each row within the array. Moreover, a decomposition processing is executed toward the elements existing within a range indicated by the created index table. Finally, a forward/backward substitution processing is executed toward the coefficient matrix elements subjected to the decomposition processing and the right-side vector elements stored into the array, thereby determining the numerical solutions.

Abstract: A method of computing shortest paths in a weighted graph having vertices and an adjacency matrix with memory resources and a processor including (a) selecting integer weights; (b) carrying out a series of incrementations, an incrementation including finding a set of vertices to which one may arrive from a given set of vertices; (c) carrying out a series of decrementations, a decrementation including finding a set of vertices from which one may go to arrive to a given set of vertices; (d) causing the incrementations and decrementations to be carried out in any order; (e) transforming vectors of increments/decrements in paths, the paths making up a set E1 of the shortest paths in term of number of arcs or using a given number of arcs, Na; (f) selecting n-uple of paths C of lowest cost among set of paths E1; (g) calculating Nb=Na+1; (h) computing iteratively, while Nb≦W(C) the following steps: i.

Abstract: One embodiment of the present invention provides a system for solving a nonlinear equation through interval arithmetic. During operation, the system receives a representation of the nonlinear equation ƒ(x)=0, as well as a representation of an initial interval, X, wherein this representation of X includes a first floating-point number, XL, for the left endpoint of X, and a second floating-point number, XU, for the right endpoint of X. Next, the system symbolically manipulates the nonlinear equation ƒ(x)=0 to solve for a first term, g1(x), thereby producing a modified equation g1(x)=h1(x), wherein the first term g1(x) can be analytically inverted to produce an inverse function g1−1(x). The system then plugs the initial interval X into the modified equation to produce the equation g1(X′)=h1(X), and solves for X′=g1−1[h1(X)].

Abstract: In one embodiment, a system and method for solving linear programs includes a perceptron algorithm configured to move toward a solution to the linear program. A transform algorithm is configured to stretch portions of a vector space within which the linear program is defined. A decision module decides between continued application of the perceptron algorithm and application of the transform algorithm based on a rate at which the approximate solutions are approaching a satisfactory solution.

Abstract: An interleaver parameter generator circuit used to calculate and generate on an as needed basis interleaver parameters for interleaving blocks of information of varying lengths in accordance with a pseudorandom pattern defined by the 3GPP standard. The interleaver parameter generator circuit calculates and generates the defined interleaver parameters based on an input parameter that represents the length of the block of information to be interleaved. At least one of the defined parameters is calculated and generated using a decomposed form of its definition. The interleaver parameter generator circuit uses well known circuit blocks such as multipliers, subtractors, Compare-and-Select circuits and other circuits to calculate and generate the defined parameters.

Abstract: Elements of a vector sequence A·&phgr;m are sampled to be stored in a memory. In this sampling, a combination of spatial sampling and local sampling on the basis of physical phenomenon is employed. A residual minimization coefficient &agr;1m (wherein l=1, . . . , L) used for obtaining a corrected approximate value &phgr;m is approximately obtained by using elements of a vector sequence A·&phgr;k (wherein k=m−L+1, . . . , m−1) stored in the memory.

Abstract: Matrix element calculation carried out efficiently without the overhead of communication between a host computer and processor elements even in parallel calculation utilizing a low-cost communication device and multiple processor elements having memories of a small capacity. In a method for calculating molecular orbitals, for example, all elements F(I, J) of a Fock matrix are calculated where an outermost loop is a loop associated with combinations (RT) of contracted shell R and contracted shell T which satisfy relationships R≦Nshell and T≦R. A second loop is a loop associated with contracted shell S, and a third loop is a loop associated with contracted shell U. Alternatively, the second loop is a loop associated with the contracted shell U, and the third loop is a loop associated with the contracted shell S. The value of S ranges from 1 to R, and the value of U ranges from 1 to R.

Abstract: In a preconditioning process for an iteration method to solve simultaneous linear equations through multilevel block incomplete factorization of a coefficient matrix, a set of variable numbers of variables to be removed is determined at each level of the factorization such that a block matrix comprising coefficients of the variables can be diagonal dominant. The approximate inverse matrix of the block matrix is obtained in iterative computation, and non-zero elements of a coefficient matrix at a coarse level are reduced.

Abstract: Diagonal elements of a triangular matrix are stored in memories 12 and 17, a computation using an output from each of shift stages REG1 to REG(N-1) of a shift register 11 and a diagonal element output from the memory 12 is performed, a computation result is input to the shift register 11, computation processing using a new register output from each of shift stages REG1 to REG(N-1) of the shift register 11 and the diagonal element output from the memory 12 is cyclically repeated, thereby solving a simultaneous linear equation.

Abstract: A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by a physical quantity U, is solved by successive approximation. In calculation, (f−A·Um−B(Um)) is given as a nonlinear residual rr of an approximate solution Um, wherein m is the number of repeating times, and the approximate solution Um is repeatedly corrected so as to reduce a norm of a nonlinear residual rm+1 employed in a subsequent step.

Abstract: One embodiment of the present invention provides a system that uses a block-partitioned technique to efficiently solve a system of linear equations. The system first receives a matrix that specifies the system of linear equations to be used in performing a time-based simulation. This matrix includes a static portion containing entries that remain fixed over multiple time steps in the time-based simulation, as well as a dynamic portion containing entries that change between time steps in the time-based simulation. Next, the system performs the time-based stimulation, wherein performing the time-based simulation involves solving the system of linear equations for each time step in the time-based simulation. In solving the system of linear equations, the system factorizes the static portion of the matrix only once, and reuses the factorization of the static portion in performing an overall factorization of the matrix for each time step of the time-based simulation.

Abstract: The present invention provides a method and system that produces a near-optimum schedule in linear time by providing an optimal resource ordering scheme. The present invention is embodied in a scheduling computer program.

Abstract: A method for solving a system of N linear equations in N unknown variables.

Abstract: The poor scalability of existing superscalar processors has been of great concern to the computer engineering community. In particular, the critical-path delays of many components in existing implementations grow quadratically with the issue width and the window size. This patent presents a novel way to reimplement these components and reduce their critical-path delay growth. It then describes an entire processor microarchitecture, called the Ultrascalar processor, that has better critical-path delay growth than existing superscalars. Most of our scalable designs are based on a single circuit, a cyclic segmented parallel prefix (cspp). We observe that processor components typically operate on a wrap-around sequence of instructions, computing some associative property of that sequence. For example, to assign an ALU to the oldest requesting instruction, each instruction in the instruction sequence must be told whether any preceding instructions are requesting an ALU.

Abstract: A computer-based method and system comprising three data structures: partially ordered data structure (or simply ordered data structure), contiguous list v, and vector p, is used for solving a large sparse triangular system of linear equations which utilizes only the non-zero components of a matrix to solve large sparse triangular linear equations and generates explicitly only the non-zero entries of the solution. A list of the row indices of the known non-zero values of x which require further processing is stored in the ordered data structure. Actual non-zero values of x are stored in the contiguous list v and the corresponding pointers to the location of these values are stored in the vector p. The computer-based method manipulates these three matrices to find a solution to an upper or lower sparse triangular system of linear equations.

Abstract: One embodiment of the present invention provides a system that computes interval parameter bounds from fallible measurements. During operation, the system receives a set of measurements z1, . . . , zn, wherein an observation model describes each z1 as a function of a p-element vector parameter x=(xi, . . . , xp). Next, the system forms a system of nonlinear equations zi−h(x)=0 (i=1, . . . , n) based on the observation model. Finally, the system solves the system of nonlinear equations to determine interval parameter bounds on x.

Abstract: A computer method of vector operations for calculating the inverse of a general square matrix and for solving linear equations systems. The invention comprises a new method of factorization and executing multiply-add operations useful for effecting dot-product operations of one-dimensional vectors. This new method reduces the computation time over computers programmed to use prior art methods.

Abstract: The coefficient matrix, corresponding to the simultaneous linear equations to be solved, is divided into a plurality of row sets. The row sets as divided are processed in a parallel fashion, and entries specifying the nonzero elements contained in the first to nth row sets are added to the entry sets E1 to En. Moreover, in regard to each row set, fill-ins which take place at the time of eliminating the ith variable are obtained in a parallel fashion, and entries specifying the fill-ins are added to the entry sets E1 to En. The coefficient matrix is compressed using those entry sets E1 to En.

Abstract: One embodiment of the present invention provides a system that performs a procedure to solve a system of linear inequalities. During operation, the system receives a representation of the system of linear inequalities Ax≦b, wherein Ax≦b can be a linearized form of a system of nonlinear equations. Within this representation, A is an interval matrix with m rows corresponding to m inequalities, and with n columns corresponding to n variables, the vector x includes n variable components, and the vector b includes m scalar interval components. The system solves the system of linear inequalities Ax≦b by performing a Gaussian elimination process using only positive multipliers so as not to change the sense of any inequality.