Abstract: In accordance with one embodiment, a special purpose computer can be implemented for processing a linear optimization problem capable of being represented in the form [A][X]+[I][Y]=[B] and wherein the linear optimization problem can also be represented in the form [E][A][X]+[E][I][Y]=[E][B]. The computer may comprise a first processor; a plurality of row processors each configured to store a row of the matrix [E]; a computer memory in communication with the first processor and in communication with each row processor so that each row processor can read from the computer memory and write to the computer memory; wherein the first processor is configured to signal all of the row processors to process data related to the linear optimization problem.

Abstract: In accordance with one embodiment, a method of reducing computer error in processing a linear programming problem can be accomplished by obtaining a first objective function, f, to be optimized; obtaining a second objective function, h; and optimizing first objective function f and optimizing second objective function h so as to reduce computer error.

Abstract: In accordance with one embodiment, a method of processing a linear programming problem can be implemented by utilizing a unique operation known as a pivot-in-place operation to reduce computer error.

Abstract: In accordance with one embodiment of the invention, a method of optimizing a linear equation optimality problem subject to a change of conditions can be accomplished. The method can include determining a first set of conditions for the linear equation optimality problem; initiating processing by a computer to optimize the optimality problem in accordance with the first set of conditions; determining a second set of conditions different from the first set of conditions; continuing processing with the computer to optimize the optimality problem by using the second set of conditions without having to re-initialize the computer.