Sparse Matrices

Name: Sparse Matrices
Brand: Academic Press
Price: 66.95 EUR
Availability: OnlineOnly

Tewarson(Autor*in)

Tewarson(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

177 Seiten

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978-0-08-095608-4 (ISBN)

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Inhalt

Front Cover
Sparse Matrics
Copyright Page
Contents
Preface
Acknowledgments
Chapter 1. Preliminary Considerations
1.1 Introduction
1.2 Sparse Matrices
1.3 Packed Form of Storage
1.4 Scaling
1.5 Bibliography and Comments
Chapter 2. The Gaussian Elimination
2.1 Introduction
2.2 The Basic Method
2.3 Pivoting and Round-off Errors
2.4 The Elimination Form of Inverse
2.5 Minimizing the Total Number of Nonzero Elements in EFI
2.6 Storage and Use of the Elimination Form of Inverse
2.7 Bibliography and Comments
Chapter 3. Additional Methods for Minimizing the Storage for EFI
3.1 Introduction
3.2 Methods Based on A Priori Column Permutations
3.3 Desirable Forms for Gaussian Elimination
3.4 Matrices and Graphs
3.5 The Block Diagonal Form
3.6 The Block Triangular Form
3.7 The Band Triangular Form
3.8 The Band Form
3.9 Other Desirable Forms
3.10 Inverses of BTF and BBTF
3.11 Bibliography and Comments
Chapter 4. Direct Triangular Decomposition
4.1 Introduction
4.2 The Crout Method
4.3 Minimizing the Fill-in for the Crout Method
4.4 The Doolittle (Black) Method
4.5 The Cholesky (Square-Root, Banachiewicz) Method
4.6 Desirable Forms for Triangular Decomposition
4.7 Bibliography and Comments
Chapter 5. The Gnuss-Jordan Elimination
5.1 Introduction
5.2 The Basic Method
5.3 The Relationship between the PFI and the EFI
5.4 Minimizing the Total Number of Nonzeros in the PFI
5.5 Desirable Forms for the GJE
5.6 Bibliography and Comments
Chapter 6. Orthogonalization Methods
6.1 Introduction
6.2 The Gram-Schmidt Method
6.3 Minimizing the Nonzeros in the RGS Method
6.4 The Householder Triangularization Method
6.5 The Fill-in for the RGS versus the HT Method
6.6 The Jacobi Method
6.7 Bibliography and Comments
Chapter 7. Eigenvalues and Eigenvectors
7.1 Introduction
7.2 The Givens Method
7.3 The Householder Method
7.4 Reduction to the Hessenberg Form
7.5 Eigenvectors
7.6 Bibliography and Comments
Chapter 8. Change of Basis and Miscellaneous Topics
8.1 Introduction
8.2 The Result of Changes in a Column of A on A-1
8.3 Kron's Method of Tearing
8.4 Bifactorization
8.5 Bibliography and Comments
References
Author Index
Subject Index

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