A Jacobi-Davidson method for solving complex symmetric eigenvalue problems
, 2002 . We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to
E. Hochstenbach, Peter Arbenz, Michiel
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, 2008 . In this article, thequasi-Laguerre iteration is established inthe spiritofLaguerre’s iteration for solving polynomial f with all real zeros. The new algorithm, which maintains the monotonicity and global convergence of the Laguerre iteration, no longer
Siam J. Sci Comput +4 more
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Superlinear Convergence Rates For The Lanczos Method Applied To Elliptic Operators [PDF]
, 1996 . This paper investigates the convergence of the Lanczos method for computing the smallest eigenpair of a selfadjoint elliptic differential operator via inverse iteration (without shifts).
Hanke, Martin, Martin Hanke
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A new method for computing the stable invariant subspace of a real Hamiltonian matrix or: Breaking Van Loan's curse? [PDF]
, 1997 A new backward stable, structure preserving method of complexity O(n 3 ) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation.
Benner, P. +5 more
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ABLE: an Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
, 1995 . This work presents an Adaptive Block Lanczos method for large scale non-Hermitian Eigenvalue problems (henceforth the ABLE method). The ABLE method is a block version of the non-Hermitian Lanczos algorithm. There are three innovations.
Zhaojun Bai, Qiang Ye, David Day
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All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations. [PDF]
Calcolo, 2021 Donatelli M +3 more
europepmc +1 more source
On Ill-Conditioned Eigenvalues, Multiple Roots of Polynomials, and their Accurate Computations
, 1998 Algebraic eigenvalues with associated left and right eigenvectors (nearly) orthogonal, and polynomial roots that are multiple, have been known to be sensitive to perturbations in numerical computation and thereby ill-conditioned.
Zhonggang Zeng
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Two Algorithms For Symmetric Linear Systems With Multiple Right-Hand Sides
, 1998 In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and ...
Hua Dai
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COMPUTING INTERIOR EIGENVALUES OF NONLINEAR HERMITEAN EIGENVALUE PROBLEMS
, 2008 restart AMS subject classification. 65F15, 15A18, 35P30, 49R50, 65N25 Abstract. A nonlinear eigenvalue problem T(λ)x = 0, the eigenvalues of which satisfy a minmax characterization shares many valuable properties of linear Hermitean eigenvalue problems ...
Vera Lochmann +2 more
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Bisection Acceleration for the Symmetric Tridiagonal Eigenvalue Problem
, 1999 We present new algorithms that accelerate the bisection method for the symmetric tridiagonal eigenvalue problem. The algorithms rely on some new techniques, including a new variant of Newton's iteration that reaches cubic convergence (right from the
Victor Y. Pan, Elliot Linzer
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