Quadratic Eigenvalue Problem
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High Quality Content by WIKIPEDIA articles! Direct methods for solving the standard or generalized eigenvalue problems Ax = x and Ax = Bx are based on transforming the problem to Schur or Generalized Schur form. However, there is no analogous form for quadratic matrix polynomials. One approach is to transform the quadratic matrix polynomial to a linear matrix pencil (A B), and solve a generalized eigenvalue problem. Once eigenvalues and eigenvectors of the linear problem have been determined, eigenvectors and eigenvalues of the quadratic can be determined.

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High Quality Content by WIKIPEDIA articles! Direct methods for solving the standard or generalized eigenvalue problems Ax = x and Ax = Bx are based on transforming the problem to Schur or Generalized Schur form. However, there is no analogous form for quadratic matrix polynomials. One approach is to transform the quadratic matrix polynomial to a linear matrix pencil (A B), and solve a generalized eigenvalue problem. Once eigenvalues and eigenvectors of the linear problem have been determined, eigenvectors and eigenvalues of the quadratic can be determined.