کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641417 | 1341308 | 2009 | 11 صفحه PDF | دانلود رایگان |
We employ the sine transform-based preconditioner to precondition the shifted Toeplitz matrix An−ρBnAn−ρBn involved in the Lanczos method to compute the minimum eigenvalue of the generalized symmetric Toeplitz eigenvalue problem Anx=λBnxAnx=λBnx, where AnAn and BnBn 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.
Journal: Journal of Computational and Applied Mathematics - Volume 226, Issue 1, 1 April 2009, Pages 66–76