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The Lanczos algorithm applied to Kron's method
Author(s) -
Sehmi N. S.
Publication year - 1986
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.1620231006
Subject(s) - tridiagonal matrix , lanczos resampling , mathematics , eigenvalues and eigenvectors , lanczos algorithm , scalar (mathematics) , matrix (chemical analysis) , algorithm , physics , quantum mechanics , geometry , materials science , composite material
In this paper Kron's primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix. This matrix, although never formed explicitly, can then be transformed to a tridiagonal matrix of reduced order by the Lanczos algorithm. Eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system. The method has multiplication counts which are over 90 per cent lower than when the (condensed) Kron matrix is solved by the Newton‐Raphson iteration applied to the Kron scalar equation. Numerical examples illustrating the Kron‐Lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presented.