ACM Transactions on Mathematical Software (TOMS)
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
A large, sparse, and indefinite generalized eigenvalue problem from fluid mechanics
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
SIAM Journal on Matrix Analysis and Applications
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Matrix algorithms
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems
Computers & Mathematics with Applications
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The harmonic block Arnoldi method can be used to find interior eigenpairs of large matrices. Given a target point or shift @t to which the needed interior eigenvalues are close, the desired interior eigenpairs are the eigenvalues nearest @t and the associated eigenvectors. However, it has been shown that the harmonic Ritz vectors may converge erratically and even may fail to do so. To do a better job, a modified harmonic block Arnoldi method is coined that replaces the harmonic Ritz vectors by some modified harmonic Ritz vectors. The relationships between the modified harmonic block Arnoldi method and the original one are analyzed. Moreover, how to adaptively adjust shifts during iterations so as to improve convergence is also discussed. Numerical results on the efficiency of the new algorithm are reported.