Results 11 to 20 of about 1,981 (210)
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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Acceleration of implicit schemes for large systems of nonlinear differential-algebraic equations
AIMS Mathematics, 2020 When solving large systems of nonlinear differential-algebraic equations by implicit schemes, each integration step requires the solution of a system of large nonlinear algebraic equations.
Mouhamad Al Sayed Ali, Miloud Sadkane
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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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Fractal and Fractional, 2023 The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials.
Mohamed Abdelsabour Fahmy
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High-Performance GMRES Multi-Precision Benchmark
Proposed for presentation at the Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems in ,, 2023 Ichitaro Yamazaki +5 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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Modified DTS Iteration Methods for Spatial Fractional Diffusion Equations
Mathematics, 2023 For the discretized linear systems of the spatial fractional diffusion equations, we construct a class of a modified DTS iteration method and give its asymptotic convergence conditions.
Xin-Hui Shao, Chong-Bo Kang
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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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