Numerical solution of saddle point problems by block Gram--Schmidt orthogonalization

2013/12/18 by Felicja Okulicka-Dłużewska, Okulicka-Dłużewska, Felicja, Alicja Smoktunowicz +1 · 14 citations
Computer Science · Mathematics · Physics and Astronomy · #15A12 #15A23 #15A60 #65H10 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1312.5277

openalex publication_date 2013/12/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we prove that the algorithm BCGS2 (Reorthogonalized Block Classical Gram-Schmidt) using Householder Q-R decomposition implemented in floating point arithmetic is backward stable, under a mild assumption on the matrix M. This means that the computed vector z is the exact solution to a slightly perturbed linear system of equations Mz = f.

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Related

• Reorthogonalized Block Classical Gram--Schmidt
• Generalized Golub-Kahan bidiagonalization for nonsymmetric saddle point systems
• Generalized Golub-Kahan bidiagonalization for generalized saddle point systems
• Reduced Basis A Posteriori Error Bounds for Symmetric Parametrized Saddle Point Problems
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