Title Sparse matrices / Reginald P. Tewarson

Published New York : Academic Press, 1973

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Description 1 online resource (xv, 160 pages) : illustrations Series Mathematics in science and engineering ; v. 99 Mathematics in science and engineering ; v. 99. Contents 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 Introduction3.2 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 Decomposition4.7 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 CommentsChapter 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 Bibliography Includes bibliographical references (pages 141-151) and indexes Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL Print version record digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Subject Matrices -- Data processing MATHEMATICS -- Algebra -- Elementary. Matrices -- Data processing Form Electronic book ISBN 9780126856507 0126856508 9780080956084 0080956084 1282290215 9781282290211

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