A contour integral approach to the computation of invariant pairs

作者：Barkatou Moulay; Boito Paola; Ugalde Esteban Segura^*

来源：Theoretical Computer Science, 2017, 681: 3-26.

DOI：10.1016/j.tcs.2017.03.024

• Matrix polynomials
• Eigenvalues
• Invariant pairs
• Contour integral
• Moments
• Solvents
• Triangularization

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thummler [6]. Invariant pairs extend the notion of eigenvalue-eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. We compute formulations for the condition numbers and the backward error for invariant pairs and solvents. We then adapt the Sakurai-Sugiura moment method [1] to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues. Numerical refinement via a variant of Newton's method is also studied. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials.

• 出版日期2017-6-12