Conjugate gradient solvers for linear systems

摘要

Conjugate gradient solver apparatus 2 is provided for generating data defining a solution vector x for a linear system represented by Ax = b where A is a predetermined matrix and b is a predetermined vector. Solver circuitry 6 of the apparatus processes input data, defining said matrix A and vector b, in accordance with an iterative conjugate gradient method to generate said data defining the solution vector x. The solver circuitry is adapted to process data items, corresponding to vectors used in said conjugate gradientmethod, having a variable fixed-point data format. A precision controller 7 of the apparatus determines the fixed-point data formats of respective said data items adaptively during progress of the conjugate gradient method in the solver circuitry 6. The solver apparatus may be implemented by a field programmable gate array (FPGA). The adaptive fixed-point format variation allows good results to be achieved while exploiting the simple, fast, and power-efficient operations available with fixed-point processing.