Val'erie Frayss'e and Vincent Toumazou. A note on the normwise perturbation theory for the regular generalized eigenproblem. Numerical Linear Algebra with Applications, 5(1):1--10, 1998. Home/Search Document Details and Download
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Backward Error and Condition of Polynomial Eigenvalue Problems - Tisseur (2000) (9 citations) (Correct)
....all the eigenpairs are desired, or an Arnoldi or nonsymmetric Lanczos type method if only a few of them are required. This work has three main contributions. First, for the PEP, we give computable expressions for backward errors and condition numbers of simple eigenvalues by extending the work in [6] and [11] concerning the GEP. There are many ways to reformulate the PEP as a GEP. Our second contribution is to study the stability of these transformations in the case m = 2. We show that solving the QEP by applying the QZ algorithm to the GEP can be backward unstable for the QEP. Finally, we ....
Val'erie Frayss'e and Vincent Toumazou. A note on the normwise perturbation theory for the regular generalized eigenproblem. Numerical Linear Algebra with Applications, 5(1):1--10, 1998.
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