On Symmetric Positive Definite Preconditioners for Multiple Saddle-Point Systems

2021/06/23 by John W. Pearson, Pearson, John W., Andreas Potschka +1 · 1 citation
Computer Science · Physics and Astronomy · Engineering · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2106.12433

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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