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Lanczos Algorithms for Large Symmetric Eigenvalue Computations
Jane K. CullumRalph A. Willoughby
其他書名
Vol. 1: Theory
出版SIAM, 2002-09-01
主題Mathematics / AppliedMathematics / GeneralMathematics / Differential Equations / General
ISBN08987152379780898715231
URLhttp://books.google.com.hk/books?id=yfs6dzb-5zcC&hl=&source=gbs_api
EBookSAMPLE
註釋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.