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9780898715231 Academic Inspection Copy

Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Volume I

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First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge elgenvalue problems. It deals with "symmetric" problems. However, in this book, "symmetric" also encompasses numerical procedures for computing singular values and vectors of real rectangular matrices and numerical procedures for computing eigenelements of nondefective complex symmetric matrices. Although preserving orthogonality has been the golden rule in linear algebra, most of the algorithms in this book conform to that rule only locally, resulting in markedly reduced memory requirements. Additionally, most of the algorithms discussed separate the eigenvalue (singular value) computations from the corresponding eigenvector (singular vector) computations. This separation prevents losses in accuracy that can occur.
Preface Introduction Preliminaries: Notation and Definitions Chapter 1: Real 'Symmetric' Problems Chapter 2: Lanczos Procedures, Real Symmetric Problems Chapter 3: Tridiagonal Matrices Chapter 4: Lanczos Procedures with No Reorthogonalization for Real Symmetric Problems Chapter 5: Real Rectangular Matrices Chapter 6: Nondefective Complex Symmetric Matrices Chapter 7: Block Lanczos Procedures, Real Symmetric Matrices References Author and Subject Indices.
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