[PDF] Lanczos Algorithms For Large Symmetric Eigenvalue Computations Programs eBook

Author : Jane K. Cullum
Publisher : SIAM
Page : 290 pages
File Size : 49,41 MB
Release : 2002-09-01
Category : Mathematics
ISBN : 0898715237

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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 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.

Author : CULLUM
Publisher : Birkhäuser
Page : 273 pages
File Size : 21,40 MB
Release : 2012-05-06
Category : Mathematics
ISBN : 9781468491920

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Energy levels, resonanees, vibrations, feature extraetion, faetor analysis - the names vary from discipline to diseipline; however, all involve eigenvalue/eigenveetor eomputations. An engineer or physicist who is modeling a physieal proeess, strueture, or deviee is eonstrained to seleet a model for whieh the subsequently-required eomputations ean be performed. This eonstraint often leads to redueed order or redueed size models whieh may or may not preserve all of the important eharaeteristies of the system being modeled. Ideally, the modeler should not be foreed to make such apriori reduetions. It is our intention to provide here proeedures wh ich will allow the direct and suceessful solution of many large 'symmetrie' eigenvalue problems, so that at least in problems where the computations are of this type there will be no need for model reduetion. Matrix eigenelement eomputations can be c1assified as smalI, medium, or large seale, in terms of their relative degrees of difficulty as measured by the amount of computer storage and time required to eomplete the desired eomputations. A matrix eigenvalue problem is said to be sm all scale if the given matrix has order smaller than 100. Well-documented and reliable FORTRAN pro grams exist for small scale eigenelement computations, see in particular ElS­ PACK [1976,1977]. Typically those programs explicitly trans form the given matrix into a simpler canonieal form. The eigenelement eomputations are then performed on the canonical form.