A Schur-based algorithm for computing bounds to the smallest eigenvalue of a symmetric positive definite Toeplitz matrix
โ Scribed by N. Mastronardi; M. Van Barel; R. Vandebril
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 157 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
A projection method for computing the minimal eigenvalue of a symmetric and positive definite Toeplitz matrix is presented. It generalizes and accelerates the algorithm considered in [12] (W. Mackens, H. Voss, SIAM J. Matrix Anal. Appl. 18 (1997) Q-534). Global and cubic convergence is proved. Rand
Let A be a positive definite, symmetric matrix. We wish to determine the largest eigenvalue, 1,. We consider the power method, i.e. that of choosing a vector v. and setting vk = Akvo; then the Rayleigh quotients Rk = (Auk, vk)/( ok, ok) usually converge to 21 as k -+ 03 (here (u, v) denotes their in