Algorithm 37. Solution of sparse linear equation systems
F. Pankowski (1974)
Applicationes Mathematicae
K. Wrześniowski, Elżbieta Winkel (1978)
Applicationes Mathematicae
Z. Kasperski (1978)
Applicationes Mathematicae
Anna Bartkowiak (1982)
Applicationes Mathematicae
Anna Bartkowiak (1982)
Applicationes Mathematicae
Lionel Ducos (1996)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Pham Dinh Tao (1984)
Numerische Mathematik
F. Robert (1972)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
J. Roman, P. Charrier (1987)
Numerische Mathematik
Lubomír Skála (1977)
Aplikace matematiky
Jadwiga Dzikiewicz, M. M. Sysło (1978)
Applicationes Mathematicae
J. K. Baksalary, A. Dobek, R. Kala (1980)
Applicationes Mathematicae
Tommy Elfving, Ake Björck (1973)
Numerische Mathematik
P. LANCASTER (1964)
Numerische Mathematik
Laszkiewicz, Beata, Ziȩtak, Krystyna (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Tyrone Rees, Martin Stoll, Andy Wathen (2010)
Kybernetika
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
M. Dryja (1984)
Banach Center Publications
V. Conrad, Y. Wallach (1979)
Numerische Mathematik
Han, Lixing, Neumann, Michael, Prasad, Upendra (2009)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
C. Roland, B. Beckermann, C. Brezinski (2004)
Applicationes Mathematicae
We discuss two different methods of Altman for solving systems of linear equations. These methods can be considered as Krylov subspace type methods for solving a projected counterpart of the original system. We discuss the link to classical Krylov subspace methods, and give some theoretical and numerical results on their convergence behavior.