Results 11 to 20 of about 14,331 (187)
Weighted Inner Products for GMRES and GMRES-DR [PDF]
SIAM Journal on Scientific Computing, 2017 The convergence of the restarted GMRES method can be significantly improved, for some problems, by using a weighted inner product that changes at each restart. How does this weighting affect convergence, and when is it useful? We show that weighted inner
Embree, Mark +2 more
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GMRES-Accelerated ADMM for Quadratic Objectives [PDF]
SIAM Journal on Optimization, 2018 We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton subproblem of ...
White, Jacob K., Zhang, Richard Y.
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SIAM Journal on Scientific Computing, 2023 The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems $A{\bf x}={\bf b}$, with initial guess ${\bf x}_0$ and residual ${\bf r}_0 = {\bf b} - A{\bf x}_0$. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of $V_k$).
Stephen Thomas +4 more
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Toward efficient polynomial preconditioning for GMRES [PDF]
Numerical Linear Algebra with Applications, 2021 AbstractWe present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many previous polynomial preconditioners. Our current implementation of this polynomial using its roots is naturally
Jennifer A. Loe, Ronald B. Morgan
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GMRES and Integral Operators [PDF]
SIAM Journal on Scientific Computing, 1996 The purpose of this paper is to show how the generalized minimal residual (GMRES) method can be modified to incorporate Nyström interpolation at a small cost in both computational effort and algorithmic complexity. The result is an algorithm that has the convergence property of Broyden's method.
Kelley, C. T., Xue, Z. Q.
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Multipreconditioned Gmres for Shifted Systems [PDF]
SIAM Journal on Scientific Computing, 2017 An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix.
Bakhos, T. +4 more
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Adaptive version of Simpler GMRES [PDF]
Numerical Algorithms, 2009 The authors propose and theoretically analyze a stable version of simpler generalized minimal residual (GMRES) algorithm, based on an adaptive choice of the Krylov subspace basis at a given iteration step. They show that this adaptive choice of direction vectors keeps the basis well-conditioned and that the condition number grows at most linearly with ...
Jiránek, P., Rozložník, M. (Miroslav)
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GMRES On (Nearly) Singular Systems [PDF]
SIAM Journal on Matrix Analysis and Applications, 1997 The authors' purpose is to examine the behavior of the GMRES method when the matrix \(A\) is singular or nearly so, i.e., ill-conditioned, and to formulate practically effective ways of recognizing the singularity or the ill-conditioning when it might significantly affect the performance of the method.
Brown, Peter N., Walker, Homer F.
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Properties of Worst-Case GMRES [PDF]
SIAM Journal on Matrix Analysis and Applications, 2013 In the convergence analysis of the GMRES method for a given matrix $A$, one quantity of interest is the largest possible residual norm that can be attained, at a given iteration step $k$, over all unit norm initial vectors. This quantity is called the worst-case GMRES residual norm for $A$ and $k$.
Faber, Vance +2 more
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Linear Algebra and its Applications, 2003 In their introduction, the authors state, ``We study an oddity: the class of problems for which the generalized minimal residual (GMRES) algorithm, when started with the initial guess \(x^{(0)}=0\) and using exact arithmetic, computes \(m\) iterates \(x^{(1)}=\cdots=x^{(m)}=0\) without making any progress at all.
Zavorin, Ilya +2 more
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