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Eigenproblem solution by a combined Sturm sequence and inverse iteration technique
Author(s) -
Gupta K. K.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620070103
Subject(s) - eigenvalues and eigenvectors , fortran , computation , sequence (biology) , inverse , listing (finance) , algorithm , computer program , sturm–liouville theory , inverse iteration , computer science , mathematics , geometry , programming language , physics , finance , quantum mechanics , biology , economics , genetics
This article presents an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = λBq with band symmetric A and B, B being also positive definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems including free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.