Iterative incomplete factorization methods
by Ilʹin, V. P., (Valeriĭ Pavlovich)
This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which arise in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate gradients or the Chebyshev technique. Different kinds of explicit and implicit algorithms are considered. Theoretical grounds of correctness and estimates of the co…
Read More ↓Title Statements
- Full title :Iterative incomplete factorization methods / V.P. Ilín.
Summary
This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which arise in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate gradients or the Chebyshev technique. Different kinds of explicit and implicit algorithms are considered. Theoretical grounds of correctness and estimates of the convergence velocity of iterations are presented. Together with the results of experimental investigati.
Read More ↓Edition Statements
- Publication Date:1992.
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:Singapore
- Language:eng
- Publication Date:1992.
The Physical Object
- Description:1 online resource (x, 190 pages) : : illustrations
Edition Identifiers
- ISBN:9789814335881, 9814335886
- oclc:ocn841810153
- LC Classification:QA242
- Dewey Decimal:512
Table of Contents
Preface; Contents; Introduction; 1. Some Elements from Linear Algebra; 1.1. Short Extracts from Matrix Theory; 1.2. Algebraic Peculiarities of Grid Systems of Equations; 1.3. Common Properties and Comparative Analysis of Iterative Algorithms; 2. Buleev Methods and 'Grid' Principles of Incomplete Factorization; 2.1. The Explicit Buleev Method For Two-Dimensional Five-Point Equations (EBM-2); 2.2. The Explicit Buleev Method for Three-Dimensional Seven-Point Equations (EBM-3); 2.3. Examples of Other Factorizations for Two-Dimensional Problems; 2.4. Second-Order Factorization Methods.
2.5. Implicit 'Grid' Methods of Incomplete Factorization2.6. Methods of h-Factorization; 2.6.1. Tee's Method; 2.6.2. Ginkin's Method; 3. Matrix Analysis of Incomplete Factorization Methods; 3.1. Algorithms with Incomplete Triangular Factorization; 3.2. Implicit Incomplete Factorization Methods for Block Tri-Diagonal Systems; 3.2.1. Preliminaries; 3.2.2. Overimplicit Seidel Method; 3.2.3. Implicit Algorithms for Symmetric Matrices; 3.3. Application of Incomplete Factorization to Domain Decomposition Methods; 3.3.1. Domain Decomposition into Two Subdomains.
3.3.2. Domain Decomposition into Several Subdom…
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