COMPUTING EIGENVALUES OF BANDED SYMMETRICAL TOEPLITZ MATRICES

作     者：ARBENZ, P 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1991年第12卷第4期

页      面：743-754页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：TOEPLITZ MATRIX CIRCULANT MATRIX RESTRICTED EIGENVALUE PROBLEM PARALLEL COMPUTER 

摘      要：A recently proposed algorithm for the computation of the eigenvalues of symmetric banded Toeplitz matrices is investigated. The basic idea of the algorithm is to embed the Toeplitz matrix in a symmetric circulant matrix of higher order. After having computed the spectral decomposition of the circulant matrix-which is trivial since the eigenvectors of circulants are known a priori and the eigenvalues can be obtained by Fourier transform-the Toeplitz eigenvalue problem is treated as a restricted eigenvalue problem. In doing this, use can be made of the theory for intermediate problems of Weinstein and Aronszajn and its recent refinements. Since the main part of the proposed algorithm consists of independent searches for zeros in disjoint real intervals, the algorithm is well suited for parallel computers. Implementations of the algorithm are discussed and some numerical results are given. The (sequential) complexity of the computation of s eigenvalues of the Toeplitz matrix T is O(sr(n + r2)), where n is the order and r the bandwidth of T.