Augmentation-Based Preconditioners for Saddle-Point Systems with Singular Leading Blocks

06/27/2022

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by   Susanne Bradley, et al.

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We consider the iterative solution of symmetric saddle-point matrices with a singular leading block. We develop a new ideal positive definite block diagonal preconditioner that yields a preconditioned operator with four distinct eigenvalues. We offer a few techniques for making the preconditioner practical, and illustrate the effectiveness of our approach with numerical experiments.