Algorithms for Sparse Linear Systems: Nečas Center Series
Autor Jennifer Scott, Miroslav Tůmaen Limba Engleză Paperback – 30 apr 2023
Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines.
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Specificații
ISBN-13: 9783031258190
ISBN-10: 3031258193
Pagini: 242
Ilustrații: XIX, 242 p. 70 illus., 27 illus. in color.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.37 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Nečas Center Series
Locul publicării:Cham, Switzerland
ISBN-10: 3031258193
Pagini: 242
Ilustrații: XIX, 242 p. 70 illus., 27 illus. in color.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.37 kg
Ediția:1st ed. 2023
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Nečas Center Series
Locul publicării:Cham, Switzerland
Cuprins
An introduction to sparse matrices.- Sparse matrices and their graphs.- Introduction to matrix factorizations.- Sparse Cholesky sovler: The symbolic phase.- Sparse Cholesky solver: The factorization phase.- Sparse LU factorizations.- Stability, ill-conditioning and symmetric indefinite factorizations.- Sparse matrix ordering algorithms.- Algebraic preconditioning and approximate factorizations.- Incomplete factorizations.- Sparse approximate inverse preconditioners.
Notă biografică
Jennifer Scott is a Professor of Mathematics at the University of Reading and an Individual Merit Research Fellow at the Rutherford Appleton Laboratory. She is a SIAM Fellow and a Fellow of the Institute of Mathematics and its Applications. She is the author of many widely used sparse matrix packages that are available as part of the HSL Mathematical Software Library.
Miroslav Tuma is a Professor and Head of the Department of Numerical Mathematics at Charles University and was formerly a Professor at the Institute of Computer Science of the Academy of Sciences of the Czech Republic. His research has included important contributions to the development of algebraic preconditioners for iterative solvers. He was the recipient of a SIAM outstanding paper prize for his work on sparse approximate inverse preconditioners.
Textul de pe ultima copertă
Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines.
Caracteristici
This book is open access, which means that you have free and unlimited access This monograph presents factorization algorithms for solving large sparse linear systems of equations It unifies the study of direct methods and algebraic preconditioners that are traditionally treated separately. Sparse matrix algorithm outlines complement theoretical results.