Abstract: A solution method for solving an underdetermined system of linear equations, in which the number of elements of a variable to be determined is N and the number of linear equations is M (where M and N are integers satisfying 1?M<N), using iterative calculations, comprises, in each iteration: an extraction step of extracting at least M non-zero element candidates from the N elements of the variable; a subproblem solving step of setting a subproblem having only the extracted non-zero element candidates as a variable, and solving the subproblem as an ill-posed problem; and an updating step of updating values of the N elements of the variable to be determined on the basis of values of the non-zero element candidates obtained in the subproblem solving step.

Abstract: A variable to be determined is expressed as a product of a state variable and a structural variable for each element. The structural variable is a monotonically increasing function of a control variable that takes a real number value, and is thus limited to a real number of 0 to 1. An objective function defined as a function of the state variable and structural variable or the state variable and control variable is used. In each iteration, a computer executes: a state variable updating step of updating a value of each element of the state variable on the basis of information of the objective function with respect to the state variable; and a structural variable updating step of updating a value of each element of the structural variable on the basis of information of the objective function with respect to said structural variable.

Abstract: A solution method for solving an underdetermined system of linear equations, in which the number of elements of a variable to be determined is N and the number of linear equations is M (where M and N are integers satisfying 1?M<N), using iterative calculations, comprises, in each iteration: an extraction step of extracting at least M non-zero element candidates from the N elements of the variable; a subproblem solving step of setting a subproblem having only the extracted non-zero element candidates as a variable, and solving the subproblem as an ill-posed problem; and an updating step of updating values of the N elements of the variable to be determined on the basis of values of the non-zero element candidates obtained in the subproblem solving step.

Abstract: A method of optimally designing a structure includes a step of obtaining a solution of a structure optimal designing problem having a first solution process to solve an optimization problem of a first evaluation function for a status variable vector and a design variable vector, wherein the status variable vector is a displacement in each node, and the design variable vector is a rate of existence to a structural member in each element. The first solution process has a design variable update step of reading the design variable vector and the status variable vector stored in a first storage unit, updating the design variable vector, and storing the updated design variable vector into the first storage unit, and a status variable update step of reading the design variable vector and the status variable vector stored in a second storage unit, updating the status variable vector, and storing the updated status variable vector into the second storage unit.

Abstract: First, calculations to solve a given set of simultaneous linear equations are performed using a conjugate gradient method and it is determined, each time the calculations are iterated, whether or not the calculations diverge. If it is determined that the calculations diverge, the initial value of a variable is set to the minimum value and calculations to solve the set of simultaneous linear equations are performed using a conjugate residual method. This allows the set of simultaneous linear equations to be solved even if it is not known whether or not its coefficient matrix is regular.

Abstract: In an optimum design method comprising a first solution determining step of solving an optimization problem of a first evaluation function for a state variable vector with a design variable vector being as a parameter, and a second solution determining step of solving an optimization problem of a second evaluation function for the design variable vector and the state variable vector thus obtained, the second solution determining step includes the steps of computing a gradient vector of the second evaluation function for the design variable vector, computing a first coefficient based on a value of a norm of the gradient vector, computing a search vector based on the first coefficient, computing a second coefficient, and updating the design variable vector based on the second coefficient.

Abstract: A variance-covariance matrix of a matrix having a combination of multivariate data and objective variables is obtained, and multiple eigenvalues and their corresponding eigenvectors are calculated by eigenvalue decomposition of the variance-covariance matrix. Accumulated contributions are calculated from the multiple eigenvalues in descending order of absolute value of the eigenvalues. Regression coefficients are calculated from eigenvalues and eigenvectors that correspond to accumulated contributions that exceed a predetermined value.

Abstract: In an optimum design method comprising a first solution determining step of solving an optimization problem of a first evaluation function for a state variable vector with a design variable vector being as a parameter, and a second solution determining step of solving an optimization problem of a second evaluation function for the design variable vector and the state variable vector thus obtained, the second solution determining step includes the steps of computing a gradient vector of the second evaluation function for the design variable vector, computing a first coefficient based on a value of a norm of the gradient vector, computing a search vector based on the first coefficient, computing a second coefficient, and updating the design variable vector based on the second coefficient.

Abstract: In an optimum design method comprising a first solution determining step of solving an optimization problem of a first evaluation function for a state variable vector with a design variable vector being as a parameter, and a second solution determining step of solving an optimization problem of a second evaluation function for the design variable vector and the state variable vector thus obtained, the second solution determining step includes the steps of computing a gradient vector of the second evaluation function for the design variable vector, computing a first coefficient based on a value of a norm of the gradient vector, computing a search vector based on the first coefficient, computing a second coefficient, and updating the design variable vector based on the second coefficient.

Abstract: A variance-covariance matrix of a matrix having a combination of multivariate data and objective variables is obtained, and multiple eigenvalues and their corresponding eigenvectors are calculated by eigenvalue decomposition of the variance-covariance matrix. Accumulated contributions are calculated from the multiple eigenvalues in descending order of absolute value of the eigenvalues. Regression coefficients are calculated from eigenvalues and eigenvectors that correspond to accumulated contributions that exceed a predetermined value.

Abstract: First, calculations to solve a given set of simultaneous linear equations are performed using a conjugate gradient method and it is determined, each time the calculations are iterated, whether or not the calculations diverge. If it is determined that the calculations diverge, the initial value of a variable is set to the minimum value and calculations to solve the set of simultaneous linear equations are performed using a conjugate residual method. This allows the set of simultaneous linear equations to be solved even if it is not known whether or not its coefficient matrix is regular.

Abstract: A transformation unit 102 transforms an entered image to multi-resolution space. A quantizer 105 performs vector quantization on a local pattern of an image of a multi-resolution representation. A perspective-order calculating unit 107 extracts a plurality of code words, positions corresponding thereto and/or angle of rotation and/or scale, and the perspective-order relationship of a plurality of these representative vectors, from the quantized image. An algebraic encoder 108 encodes the input image based upon the extracted information. As a result, there are provided an image processing apparatus and method for asymmetric encoding without motion in three dimensions and extraction of a three-dimensional structure. Further, a transformation unit 1103 transforms an entered image to vector field, and a singularity detector 1104 detects a singularity in the transformed image.

Abstract: A solution of a structure optimal designing problem formulated as a dual optimization problem having first and second solution processes is obtained. It is assumed that a status variable vector is a displacement in each node and a design variable vector is the existence ratio of structural member in each element. At the first solution process including the second solution process as one step, stored design variable vector and status variable vector are read and the design variable vector is updated. At the second solution process, the stored design variable vector and status variable vector are read and the status variable vector is updated. A second evaluation functional of the second solution process comprises the norm of residual vector and the status variable vector is not initialized upon start of the second solution process. Further, the second solution process is performed by a conjugate gradient method.

Abstract: In an optimum design method comprising a first solution determining step of solving an optimization problem of a first evaluation function for a state variable vector with a design variable vector being as a parameter, and a second solution determining step of solving an optimization problem of a second evaluation function for the design variable vector and the state variable vector thus obtained, the second solution determining step includes the steps of computing a gradient vector of the second evaluation function for the design variable vector, computing a first coefficient based on a value of a norm of the gradient vector, computing a search vector based on the first coefficient, computing a second coefficient, and updating the design variable vector based on the second coefficient.

Abstract: A list of data of a database arranged in an order of a value of each component of a vector is formed for each component. For each component sequentially selected from base indexes, a pointer indicating data in an ascending order of a difference between data in the list and a test data is updated. Whether an end condition is satisfied or not is judged from a difference of component value between the data indicated by the pointer and the test data. If the end condition is not satisfied, whether a rejection condition is satisfied or not is judged from a distance in a partial space between the data indicated by the pointer and the test data. If the rejection condition is not satisfied, a distance in a whole space between the data indicated by the pointer and the text data is calculated. A predetermined number of data pieces are retrieved in an ascending order of a calculated distance.

Abstract: A transformation unit 102 transforms an entered image to multi-resolution space. A quantizer 105 performs vector quantization on a local pattern of an image of a multi-resolution representation. A perspective-order calculating unit 107 extracts a plurality of code words, positions corresponding thereto and/or angle of rotation and/or scale, and the perspective-order relationship of a plurality of these representative vectors, from the quantized image. An algebraic encoder 108 encodes the input image based upon the extracted information. As a result, there are provided an image processing apparatus and method for asymmetric encoding without motion in three dimensions and extraction of a three-dimensional structure. Further, a transformation unit 1103 transforms an entered image to vector field, and a singularity detector 1104 detects a singularity in the transformed image.

Abstract: A visual information processing method and apparatus for acquiring and processing visual information by successively changing the amount of visual information entered with regard to a desired target position in space, reading image data at each position at which an image is formed and storing the image data in correspondence with the target position in space. The amount of visual information is successively changed by changing the image-forming position corresponding to the target position in space by moving of the optic axis of a wide-angle lens. The visual information is successively altered by zooming or by filtering which relies upon a two-dimensional filter.

Abstract: A 2D image supplied from an image input unit including a wide view lens is sampled into a discrete form by an array sensor, and then mapped to a multi-resolution space by a 2D filter. The feature of the supplied image is detected, and then the mapped image is transformed to a local pattern about the detected feature, and then the coordinates of the position of the feature and the code word of the local pattern are formed into a set which is then encoded. The code is supplied to each cell of a stochastic automaton. The quantity of visual information is calculated in accordance with the quantity of mutual information between different cells of the stochastic automaton consisting of cells in blocks, the coordinates of the position of the feature and the distance from the feature to the optical axis so as to control the optical axis of the image input unit in such a manner that the quantity of visual information is maximized.

Abstract: In an information processing apparatus capable of communicating with a plurality of computer systems, an input interpreter separates an input character string from a user into commands and parameters, and a first degree of similarity calculating unit calculates the degree of similarity between context information representing the parameters and metadata of the computer systems. A second degree of similarity calculating unit revises the degree of similarity based upon the processing cost of a command. A command execution unit selects the computer system for which the revised degree of similarity is greatest, converts the input character string to language employed by the selected computer system, outputs the converted character string to the selected computer system and transmits the results obtained to a user terminal. Thus, a computer best suited to execution of processing can be selected from a plurality of computers connected by a network without requiring that the user make any designations.

Abstract: In order to output a predetermined number of candidate data elements similar to an inquiry vector from a set of data in a vector form stored in a database, a list of data in which data of a database is arranged in a descending order of the intensity of one component of a vector is created for each component. Then, an inquiry vector, and a metric tensor that defines the inner product of the inquiry vector and the data are input. A score based on a value such that the order in the list for each of the components is subtracted from the predetermined number and the component of the inquiry vector for the components in the inner product is added for all the components with respect to each data. The predetermined number of data elements is output on the basis of the score.