Fast Enclosure for All Eigenvalues and Invariant Subspaces in Generalized Eigenvalue Problems
Shinya Miyajima · SIAM Journal on Matrix Analysis and Applications · 2014
Two fast algorithms for enclosing all eigenvalues and invariant subspaces in generalized eigenvalue problems are proposed. In these algorithms, individual eigenvectors and invariant subspaces are enclosed when eigenvalues are well separated and closely clustered, respectively. The first algorithm involves only cubic complexity and automatically determines eigenvalue clusters. The second algorithm is applicable even for defective eigenvalues. Numerical results show the properties of the proposed algorithms.