A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436703" target="_blank" >RIV/00216208:11320/21:10436703 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z_p0rU4492" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z_p0rU4492</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-021-01245-z" target="_blank" >10.1007/s11075-021-01245-z</a>

Result language
angličtina
Original language name
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block
Original language description
Null-space methods have long been used to solve large sparse nxn symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on the case where the (1, 1) block is ill conditioned or rank deficient and the k x k (2, 2) block is non zero and small (k n). Additionally, the (2, 1) block may be rank deficient. Such systems arise in a range of practical applications. A novel nullspace approach is proposed that transforms the system matrix into a nicer symmetric saddle point matrix of order n that has a non zero (2, 2) block of order at most 2k and, importantly, the (1, 1) block is symmetric positive definite. Success of any null-space approach depends on constructing a suitable null-space basis. We propose methods for wide matrices having far fewer rows than columns with the aim of balancing stability of the transformed saddle point matrix with preserving sparsity in the (1, 1) block. Linear least squares problems that contain a small number of dense rows are an important motivation and are used to illustrate our ideas and to explore their potential for solving large-scale systems.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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