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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):131-144; doi:10.1093/qjmam/1.1.131
© 1948 by Oxford University Press
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IMPROVEMENT OF AN APPROXIMATE SET OF LATENT ROOTS AND MODAL COLUMNS OF A MATRIX BY METHODS AKIN TO THOSE OF CLASSICAL PERTURBATION THEORY

H. A. JAHN

( University of Birmingham )

A method is described for simultaneously improving all the latent roots and modal columns of a given matrix, starting from a given complete set of approximate modal columns. It is considered that the method will be useful as a final step in any iteration process of determining these quantities. The method is illustrated by a numerical example. The modification needed when two or more of the latent roots are coincident, or nearly so, is very briefly indicated. The fundamental formulae are akin to those of classical perturbation theory, the corresponding formulae of which, for the special case of a Lagrange frequency equation, are given for convenience in the Appendix.


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