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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

90

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

29

Strana od-do

1639-1667

Kód UT WoS článku

000741876100001

EID výsledku v databázi Scopus

2-s2.0-85122807545