Krylov subspace methods for large-scale matrix problems in control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
The block Lanczos method for linear systems with multiple right-hand sides
Applied Numerical Mathematics
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems
Journal of Computational and Applied Mathematics
Updating the QR decomposition of block tridiagonal and block Hessenberg matrices
Applied Numerical Mathematics
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Journal of Computational and Applied Mathematics
Deflated block Krylov subspace methods for large scale eigenvalue problems
Journal of Computational and Applied Mathematics
Backward errors for eigenproblem of two kinds of structured matrices
Journal of Computational and Applied Mathematics
Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
SIAM Journal on Scientific Computing
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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. First, an adaptive blocksize scheme cures (near) breakdown and adapts the blocksize to the order of multiple or clustered eigenvalues. Second, stopping criteria are developed that exploit the semiquadratic convergence property of the method. Third, a well-known technique from the Hermitian Lanczos algorithm is generalized to monitor the loss of biorthogonality and maintain semibiorthogonality among the computed Lanczos vectors. Each innovation is theoretically justified. Academic model problems and real application problems are solved to demonstrate the numerical behaviors of the method.