Breakdown-free GMRES for Singular Systems
نویسندگان
چکیده
GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsingular matrix. When the matrix is singular, GMRES may break down before an acceptable approximate solution has been determined. This paper discusses properties of GMRES solutions at breakdown and presents a modification of GMRES to overcome the breakdown.
منابع مشابه
GGMRES: A GMRES--type algorithm for solving singular linear equations with index one
In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...
متن کاملSpectral behaviour of GMRES applied to singular systems
The purpose of this paper is to develop a spectral analysis of the Hessenberg matrix obtained by the GMRES algorithm used for solving a linear system with a singular matrix. We prove that the singularity of the Hessenberg matrix depends on the nature of A and some others criteria like the zero eigenvalue multiplicity and the projection of the initial residual on particular subspaces. We also in...
متن کاملGmres on (nearly) Singular Systems
We consider the behavior of the GMRES method for solving a linear system Ax = b when A is singular or nearly so, i.e., ill conditioned. The (near) singularity of A may or may not affect the performance of GMRES, depending on the nature of the system and the initial approximate solution. For singular A, we give conditions under which the GMRES iterates converge safely to a least-squares solution...
متن کاملA Modiication to the Gmres Method for Ill-conditioned Linear Systems
This paper concerns the use of a method for the solution of ill-conditioned linear systems. We show that the Generalized Minimum Residual Method (GMRES) in conjunction with a truncated singular value decomposition can beused to solve large nonsymmetric linear systems of equations which are nearly singular. Error bounds are given for the right s i n g u l a r v ectors and singular values compute...
متن کاملAn Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices
We apply algebraic multigrid (AMG) as a preconditioner for solving large singular linear systems of the type (I−T T )x = 0 with GMRES. Here, T is assumed to be the transition matrix of a Markov process. Although AMG and GMRES are originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 26 شماره
صفحات -
تاریخ انتشار 2005