Patent ID: 9032006
Filing Date: 2015-05-12
Classification: G06F

Abstract:
1. Apparatus for generating in high-precision data elements corresponding to an n×1 vector x satisfying Ax=b where A is a symmetric, positive-definite n×n matrix corresponding to n×n predefined high-precision data elements and b is an n×1 vector corresponding to n predefined high-precision data elements, the apparatus comprising memory for storing input data defining said data elements of matrix A and of vector b, and a processor implementing control logic adapted to: (a) implement a first iterative process for generating from said input data in low-precision data elements corresponding to an n×1 vector x (b) convert the data elements of vector x (c) implement a second iterative process for generating n low-precision data elements corresponding to an n×1 correction vector dependent on the difference between the vector b and the vector product Ax, the control logic terminating the second iterative process on occurrence of a second convergence condition; wherein a vector product of the matrix A (d) produce from the n low-precision data elements of said correction vector respective high-precision data elements of an n×1 update vector u; (e) update the data elements of said current solution vector x such that x=x+u; and (f) perform steps (c) to (e) until occurrence of a third convergence condition, said input data defining the data elements of matrix A comprising a function F defining application of each matrix A element a(i,j) on an element of any n×1 vector, where 1≦i≦n and 1≦j≦n are the row and column indices respectively of matrix A elements, the control logic being adapted to use said function F in performance of steps (a) to (e) without having to form said matrix A, wherein processing operations for solving linear systems of equations involving said matrix A elements a(i,j) are performed in said memory, and memory accesses resulting from generation of a matrix vector product with matrix A is substantially reduced.