Quadratic eigenvalue problem: Difference between revisions

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Revision as of 04:44, 25 April 2008

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Rev., 43 (2001), pp. 235–286.</ref> (QEP)''', sometimes called a '''quadratic matrix equation''', is to find [[scalar]] [[eigenvalue]]s <math>\lambda\,</math>, left [[eigenvector]]s <math>y\,</math> and right eigenvectors <math>x\,</math> such that

:<math> Q(\lambda)x = 0\text{ and }y^\astQast Q(\lambda) = 0,\, </math>

where <math>Q(\lambda)=\lambda^2 A_2 + \lambda A_1 + A_0\,</math>, with matrix coefficients <math>A_2\,</math>, <math>A_1\,</math> and <math>A_0\,</math> that are of dimension <math>n\,</math>-by-<math>n\,</math>. There are <math>2n\,</math> eigenvalues that may be ''infinite'' or finite, and possibly zero. This is a special case of a [[nonlinear eigenproblem]].