Controlling Inner Iterations in the Jacobi–Davidson Method
نویسندگان
چکیده
منابع مشابه
Controlling Inner Iterations in the Jacobi-Davidson Method
The Jacobi–Davidson method is an eigenvalue solver which uses the iterative (and in general inaccurate) solution of inner linear systems to progress, in an outer iteration, towards a particular solution of the eigenproblem. In this paper we prove a relation between the residual norm of the inner linear system and the residual norm of the eigenvalue problem. We show that the latter may be estima...
متن کاملInner iterations in eigenvalue solvers
We consider inverse iteration-based eigensolvers, which require at each step solving an “inner” linear system. We assume that this linear system is solved by some (preconditioned) Krylov subspace method. In this framework, several approaches are possible, which differ by the linear system to be solved and/or the way the preconditioner is used. This includes methods such as inexact shift-and-inv...
متن کاملConvergence of Inner/outer Source Iterations with Finite Termination of the Inner Iterations
A two-stage (nested) iteration strategy, in which the outer iteration is analogous to a block Gauss-Seidel method and the inner iteration to a Jacobi method for each of these blocks, often are used in the numerical solution of discretized approximations to the neutron transport equation. This paper is concerned with the effect, within a continuous space model, of errors from finite termination ...
متن کاملInner and Outer Iterations for the Chebyshev Algorithm
We analyze the Chebyshev iteration in which the linear system involving the splitting matrix is solved inexactly by an inner iteration. We assume that the tolerance for the inner iteration may change from one outer iteration to the other. When the tolerance converges to zero, the asymptotic convergence rate is unaaected. Motivated by this result, we seek the sequence of tolerance values that yi...
متن کاملThe Role of the Inner Product in Stopping Criteria for Conjugate Gradient Iterations
Two natural and efficient stopping criteria are derived for conjugate gradient (CG) methods, based on iteration parameters. The derivation makes use of the inner product matrix B defining the CG method. In particular, the relationship between the eigenvalues and B-norm of a matrix is investigated, and it is shown that the ratio of largest to smallest eigenvalues defines the B-condition number o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2009
ISSN: 0895-4798,1095-7162
DOI: 10.1137/080732110