Parallel solution of symmetric positive definite systems with hyperbolic rotations

Abstract

An algorithm based on hyperbolic rotations is presented for the solution of linear systems of equations Ax = b, with symmetric positive definite coefficient matrix A. Forward elimination and backsubstitution are replaced by matrix-vector multiplications, rendering the method amenable to implementation on a variety of parallel and vector machines. This method can be simplified and formulated without square roots if A is also Toeplitz; a systolic (VLSI) architecture implementing the resulting recurrence equations is more efficient than previously proposed pipelined Toeplitz system solvers. The hardware count becomes independent of the matrix size if its inverse is banded.