Augmented GMRES-type methods
نویسندگان
چکیده
منابع مشابه
Augmented GMRES-type methods
GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsymmetric matrix. The method generates a Krylov subspace in which an approximate solution is determined. We present modifications of the GMRES and the closely related RRGMRES methods that allow augmentation of the Krylov subspaces generated by these methods by a user-supplied subspace. We ...
متن کاملGmres-type Methods for Inconsistent Systems
Throughout this paper the integer l is defined by (1.3). Saad and Schulz [6, Proposition 2] show that when A is nonsingular and m ≥ l, the solution xm of the minimization problem (1.2) solves the linear system (1.1). The GMRES method is often implemented by first computing an orthogonal basis {vj} min{m,l} j=1 of the Krylov subspace Km(A, r0) by Arnoldi’s method; see Saad [7] or Saad and Schult...
متن کاملSome Remarks on the Restarted and Augmented Gmres Method
Starting from the residual estimates for GMRES formulated by many authors, usually in terms of the quotient of the Hermitian part and the norm of a matrix or by using the field of values of a matrix, we present more general estimates which hold also for restarted and augmented GMRES. Sufficient conditions for convergence are formulated. All estimates are independent on the choice of an initial ...
متن کاملA Restarted Gmres Method Augmented with Eigenvectors * Ronald
The GMRES method for solving nonsymmetric linear equations is generally used with restarting to reduce storage and orthogonalization costs. Restarting slows down the convergence. However, it is possible to save some important information at the time of the restart. It is proposed that approximate eigenvectors corresponding to a few of the smallest eigenvalues be formed and added to the subspace...
متن کاملGMRES Methods for Least Squares Problems
The standard iterative method for solving large sparse least squares problems min ∈Rn ‖ −A ‖2, A ∈ Rm×n is the CGLS method, or its stabilized version LSQR, which applies the (preconditioned) conjugate gradient method to the normal equation ATA = AT . In this paper, we will consider alternative methods using a matrix B ∈ Rn×m and applying the Generalized Minimal Residual (GMRES) method to min ∈R...
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: Numerical Linear Algebra with Applications
سال: 2007
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.518