Computing thr minimum eigenvalue of a symmetric positive definite Toeplitz matrix
SIAM Journal on Scientific and Statistical Computing
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Preconditioning the Lanczos algorithm for sparse symmetric eigenvalue problems
SIAM Journal on Scientific Computing
Applied numerical linear algebra
Applied numerical linear algebra
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
SIAM Journal on Scientific Computing
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
| Hi-index | 7.29 |
We employ the sine transform-based preconditioner to precondition the shifted Toeplitz matrix A"n-@rB"n involved in the Lanczos method to compute the minimum eigenvalue of the generalized symmetric Toeplitz eigenvalue problem A"nx=@lB"nx, where A"n and B"n are given matrices of suitable sizes. The sine transform-based preconditioner can improve the spectral distribution of the shifted Toeplitz matrix and, hence, can speed up the convergence rate of the preconditioned Lanczos method. The sine transform-based preconditioner can be implemented efficiently by the fast transform algorithm. A convergence analysis shows that the preconditioned Lanczos method converges sufficiently fast, and numerical results show that this method is highly effective for a large matrix.