A New Quotient and Iterative Detection Method in an Affine Krylov Subspace for Solving Eigenvalue Problems

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Preconditioned Krylov Subspace Methods for Eigenvalue Problems

Solving Large-scale Quadratic Eigenvalue Problems with Hamiltonian Eigenstructure Using a Structure-preserving Krylov Subspace Method

We consider the numerical solution of quadratic eigenproblems with spectra that exhibit Hamiltonian symmetry. We propose to solve such problems by applying a Krylov-Schur-type method based on the symplectic Lanczos process to a structured linearization of the quadratic matrix polynomial. In order to compute interior eigenvalues, we discuss several shift-and-invert operators with Hamiltonian str...

Solving Ill-Posed Cauchy Problems by a Krylov Subspace Method

We study the numerical solution of a Cauchy problem for a self-adjoint elliptic partial differential equation uzz − Lu = 0 in three space dimensions (x, y, z) , where the domain is cylindrical in z. Cauchy data are given on the lower boundary and the boundary values on the upper boundary is sought. The problem is severely illposed. The formal solution is written as a hyperbolic cosine function ...

Eigenvalue Perturbation and Generalized Krylov Subspace Method

In this paper, we study the computational aspect of eigenvalue perturbation theory. In previous research, high order perturbation terms were often derived from Taylor series expansion. Computations based on such an approach can be both unstable and highly complicated. We present here with an approach based on the diierential formulation of perturbation theory where the high order perturbation c...