Efficient Parallel Solution of Linear Systems with Hyperbolic Rotations.
Jean-Marc Delosme, Ilse C. F. Ipsen · Defense Technical Information Center (DTIC) · 1984
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 most amenable to implementation on a variety of parallel and vector machines. The stability behaviour compares favourably with that of the best, known methods. The method can be simplified and formulated without square roots if A is also Toeplitz; a corresponding systolic architecture (in very large scale integrated circuits) for 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.