Numerical solution to a linear equation with tensor product structure

Summary We consider the numerical solution of a c-stable linear equation in the tensor product space Rn1×⋯×nd, arising from a discretized elliptic partial differential equation in Rd. 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 O(∑ini)+O(ns) computational complexity, under appropriate assumptions (with ns being the flop count for solving a linear system associated with Ai−γIni). Illustrative numerical examples will be presented.

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