多項式固有値問題における櫻井-杉浦法に対するバランシング及びスケーリング手法の研究

筑波大学 (University of Tsukuba)201

A contour integral approach to the computation of invariant pairs

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thümmler [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

第一原理実空間伝導計算手法の開発とその応用

筑波大学 (University of Tsukuba)201