Lancaster, Peter; Matematični kolokvij julij 2010

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A dilated form for the quadratic eigenvalue problems

Peter Lancaster

University of Calgary, Kanada

8. julij 2010

The quadratic eigenvalue problem concerns three square coefficient matrices of size n. It will be shown how this problem can be re-formulated in terms of three homogeneous parameters and coefficient matrices of size 2n. This has the advantage of replacing defective eigenvalues of the first problem by semisimple eigenvalues in the dilated system. This and other properties lead to a possibly competitive eigenvalue algorithm of Rayleigh quotient type.

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