کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6422623 | 1632028 | 2014 | 6 صفحه PDF | دانلود رایگان |
In this paper we study the problem of complete stagnation of the generalized minimum residual (GMRES) method for normal matrices. We first characterize all nÃn nonsingular normal matrices A such that GMRES(A,b) stagnates completely for some vector b. Also we give necessary and sufficient conditions for the non-existence of a real stagnation vector for real normal matrices. The number of real stagnation vectors for normal matrices is studied. Moreover, we characterize all the eigenvalues of nonsingular normal matrices AâM3(C) such that GMRES(A,b) stagnates completely for some bâC3. Using the results derived by A. Greenbaum, V. Pták and Z. StrakoÅ¡ in 1996, we consider the complete stagnation of unitary matrices and derive another characterization for all nonsingular normal matrices AâM3(R) such that GMRES(A,b) stagnates completely for some vector bâR3.
Journal: Journal of Computational and Applied Mathematics - Volume 263, June 2014, Pages 417-422