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arXiv · 2106.12433

On Symmetric Positive Definite Preconditioners for Multiple Saddle-Point Systems

John W. Pearson·Andreas Potschka
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Abstract

We consider symmetric positive definite preconditioners for multiple saddle-point systems of block tridiagonal form, which can be applied within the MINRES algorithm. We describe such a preconditioner for which the preconditioned matrix has only two distinct eigenvalues, 1 and -1, when the preconditioner is applied exactly. We discuss the relative merits of such an approach compared to a more widely studied block diagonal preconditioner, specify the computational work associated with applying the new preconditioner inexactly, and survey a number of theoretical results for the block diagonal case. Numerical results validate our theoretical findings.

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John W. Pearson, Andreas Potschka. 2021-06-23. On Symmetric Positive Definite Preconditioners for Multiple Saddle-Point Systems. https://arxiv.org/abs/2106.12433

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