An error bound for the preconditioned simultaneous displacement method

摘要

Suppose Ax = b is a system of linear equations where the matrix A is symmetric positive definite and consistently-ordered. A bound for the norm of the errors εk = x − xk of the PSD method in terms of the norms of δk = xk − xk−1, δk+1 = xk+1 − xk and their inner product is derived.