Numerical solution to a linear equation with tensor product structure

Abstract

SummaryWe consider the numerical solution of a c‐stable linear equation in the tensor product space , arising from a discretized elliptic partial differential equation in . Utilizing the stability, we produce an equivalent d‐stable generalized Stein‐like equation, which can be solved iteratively. For large‐scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of computational complexity, under appropriate assumptions (with ns being the flop count for solving a linear system associated with ). Illustrative numerical examples will be presented.