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

2022/06/27 by Bradley, Susanne, Greif, Chen
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2206.13624

Abstract

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.

Related

• On Symmetric Positive Definite Preconditioners for Multiple Saddle-Point Systems
• Ideal Preconditioners for Saddle Point Systems with a Rank-Deficient Leading Block
• Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization
• Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices
• On the generalized shift-splitting preconditioner for saddle point\n problems