Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Volume I

Erscheinungsjahr 2002
ISBN: 978-0-89871-523-1
Verlag: SIAM - Society for Industrial and Applied Mathematics

Buch, Englisch, Band 41, 184 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 401 g

Reihe: Classics in Applied Mathematics

First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book 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 in methods which, in order to be able to compute further into the spectrum, use successive implicit deflation by computed eigenvector or singular vector approximations.

Autoren/Hrsg.

Cullum, Jane

Cullum, Jane K.

Willoughby, Ralph A.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface; Introduction; Preliminaries: notation and definitions; 1. Real 'symmetric' problems; 2. Lanczos procedures, real symmetric problems; 3. Tridiagonal matrices; 4. Lanczos procedures with no reorthogonalization for real symmetric problems; 5. Real rectangular matrices; 6. Nondefective complex symmetric matrices; 7. Block Lanczos procedures, real symmetric matrices; References; Author and subject indices.