Results 161 to 170 of about 4,826 (176)

A new variant of restarted GMRES

Numerical Linear Algebra with Applications, 1999
The topic of this paper is a new variant of restarted generalized minimal residual (GMRES) method for solving large linear systems. The author gives an alternative form of minimal residual condition based on the construction of a polynomial which is smaller than GMRES residual one near the origin and this is used in the case of slow convergence of the ...
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A Generalized GMRES Iterative Method

2001
We describe a generalization of the GMRES iterative method in which the residual vector is no longer minimized in the 2-norm but in a C-norm, where C is a symmetric positive definite matrix. The resulting iterative method call GGMRES is derived in detail and the minimizing property is proven.
David R. Kincaid, Jen-Yuan Chen, David M. Young   +2 more
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Expressions and Bounds for the GMRES Residual

BIT Numerical Mathematics, 2000
The author discusses the generalized minimal residual method (GMRES) for the iterative solution of a linear system and derives expressions and bounds for the residual norm in this algorithm. The minimal residual norm is expressed in terms of the pseudo-inverse of the next Krylov matrix. The minimal residual norm of a scaled Jordan block is expressed in
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Shifted GMRES for oscillatory integrals

Numerische Mathematik, 2009
By applying the generalized minimal residual (GMRES) algorithm to a shifted linear differential operator, the author constructs a new method for approximating the oscillatory integral \(\int_a^b f(x)e^{i\omega g(x)}dx\). Unlike the existing methods, this one satisfies simultaneously the following properties: it has high asymptotic order and stability ...
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On the role of orthogonality in the GMRES method

1996
In the paper we deal with some computational aspects of the Generalized minimal residual method (GMRES) for solving systems of linear algebraic equations. The key question of the paper is the importance of the orthogonality of computed vectors and its influence on the rate of convergence, numerical stability and accuracy of different implementations of
Miroslav Rozlozník, Zdenek Strakos, Miroslav Tuma   +2 more
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On the Residual Norm in FOM and GMRES

SIAM Journal on Matrix Analysis and Applications, 2011
We provide expressions for the residual norms when using the full orthogonalization method and the generalized minimum residual method for solving linear systems. They involve a triangular submatrix of the Hessenberg matrix generated by the Arnoldi process.
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The superlinear convergence behaviour of GMRES

Journal of Computational and Applied Mathematics, 1993
Cornelis Vuik, H A van der Vorst
exaly  

Restarted GMRES preconditioned by deflation

Journal of Computational and Applied Mathematics, 1996
Kevin Burrage, Jocelyne Erhel
exaly  

A Flexible Inner-Outer Preconditioned GMRES Algorithm

SIAM Journal of Scientific Computing, 1993
Youcef Saad
exaly  

GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems

SIAM Journal of Scientific Computing, 1994
Anne Greenbaum
exaly