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Solving eigenvalue problems by implicit decomposition
Author(s) -
Luo JennChing
Publication year - 1991
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690070203
Subject(s) - eigenvalues and eigenvectors , mathematics , divide and conquer eigenvalue algorithm , decomposition , algebraic number , algebra over a field , algebraic equation , pure mathematics , mathematical analysis , nonlinear system , ecology , physics , quantum mechanics , biology
Abstract This paper presents three innovative methods for solving eigenvalue problems for differential equations based upon the techniques of implicit decomposition developed by Luo and Friedman. An eigenvalue problem can be written as an approximate algebraic system of the form [ K ]{X} + λ[ M ]{ X } = 0 by employing finite elements. These methods provide robust techniques to compute the real eigenpair, λ and { X }, where [ K ] and [ M ] can be asymmetric, indefinite, and even singular.