Recursive blocked algorithms for linear systems with Kronecker product structure

Minhong Chen; Daniel Kressner

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arXiv · 1905.09539

Recursive blocked algorithms for linear systems with Kronecker product structure

Minhong Chen·Daniel Kressner

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Abstract

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of generalized Sylvester matrix equations, as they arise from the discretization of PDEs with separable coefficients or the approximation of certain models in macroeconomics. By combining recursions with a mechanism for merging dimensions, an efficient algorithm is derived that outperforms existing approaches based on Sylvester solvers.

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Minhong Chen, Daniel Kressner. 2019-05-23. Recursive blocked algorithms for linear systems with Kronecker product structure. https://arxiv.org/abs/1905.09539

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