In this paper, we establish a convergence result of the cyclic reduction （CR） algorithm for a class of weakly overdamped quadratic matrix polynomials without assumption that the partial multiplicities of the nth lar...In this paper, we establish a convergence result of the cyclic reduction （CR） algorithm for a class of weakly overdamped quadratic matrix polynomials without assumption that the partial multiplicities of the nth largest eigenvalue are all equal to 2. Our result can be regarded as a complement of that by Guo, Higham and Tisseur [SIAM J. Matrix Anal. Appl., 30 （2009）, pp. 1593-1613]. The numerical example indicates that the convergence behavior of the CR algorithm is largely dictated by our theory.Mathematics subject classification： 15A24, 15A48.展开更多
Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyc...Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.展开更多
文摘In this paper, we establish a convergence result of the cyclic reduction （CR） algorithm for a class of weakly overdamped quadratic matrix polynomials without assumption that the partial multiplicities of the nth largest eigenvalue are all equal to 2. Our result can be regarded as a complement of that by Guo, Higham and Tisseur [SIAM J. Matrix Anal. Appl., 30 （2009）, pp. 1593-1613]. The numerical example indicates that the convergence behavior of the CR algorithm is largely dictated by our theory.Mathematics subject classification： 15A24, 15A48.
文摘Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.
