Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Authors: Iveta Hnětynková, M. Plešinger
Publication year: 2015
Publication type: Článek v odborném periodiku
Periodical: Linear Algebra and Its Applications
Projects: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications
Bibliographic citation: HNĚTYNKOVÁ, Iveta, PLEŠINGER, M. Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices. Linear Algebra and Its Applications. 2015, 487(15 December), 203-219. ISSN 0024-3795. E-ISSN 1873-1856
Dostupné z: doi:10.1016/j.laa.2015.09.017
DOI: 10.1016/j.laa.2015.09.017
ID: 448099

Abstract

The paper by I. Hnětynková et al. (2015) [11] introduces real wedge-shaped matrices that can be seen as a generalization of Jacobi matrices, and investigates their basic properties. They are used in the analysis of the behavior of a Krylov subspace method: The band (or block) generalization of the Golub–Kahan bidiagonalization. Wedge-shaped matrices can be linked also to the band (or block) Lanczos method. In this paper, we introduce a complex generalization of wedge-shaped matrices and show some further spectral properties, complementing the already known ones. We focus in particular on nonzero components of eigenvectors.