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- W37213052 abstract "In this thesis, we consider polynomial eigenvalue problems. We extend results oneigenvalue and eigenvector condition numbers of matrix polynomials to conditionnumbers with perturbations measured with a weighted Frobenius norm. We derivean explicit expression for the backward error of an approximate eigenpair of amatrix polynomial written in homogeneous form. We consider structured eigenvaluecondition numbers for which perturbations have a certain structure suchas symmetry, Hermitian or sparsity. We also obtain explicit and/or computableexpressions for the structured backward error of an eigenpair.We present a robust implementation of the HZ (or HR) algorithm for symmetricgeneralized eigenvalue problems. This algorithm has the advantage of preservingpseudosymmetric tridiagonal forms. It has been criticized for its numericalinstability. We propose an implementation of the HZ algorithm that allows stabilityin most cases and comparable results with other classical algorithms for illconditioned problems. The HZ algorithm is based on the HR factorization, anextension of the QR factorization in which the H factor is hyperbolic. This yieldsus to the sensitivity analysis of hyperbolic factorizations." @default.
- W37213052 created "2016-06-24" @default.
- W37213052 creator A5072692041 @default.
- W37213052 date "2005-08-01" @default.
- W37213052 modified "2023-09-27" @default.
- W37213052 title "The Polynomial Eigenvalue Problem" @default.
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