Search Results - "Sleijpen, Gerard L.G."

On the use of harmonic Ritz pairs in approximating internal eigenpairs by Sleijpen, Gerard L.G., Eshof, Jasper van den

“…The goal of this paper is to increase our understanding of harmonic Rayleigh–Ritz for real symmetric matrices. We do this by discussing different, though…”
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Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach by Abe, Kuniyoshi, Sleijpen, Gerard L.G.

“…The Induced Dimension Reduction(s) (IDR(s)) method has recently been developed. Sleijpen et al. have reformulated the Bi-Conjugate Gradient STABilized…”
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Fast design of local N-gram-specific absorption rate-optimized radiofrequency pulses for parallel transmit systems by Sbrizzi, Alessandro, Hoogduin, Hans, Lagendijk, Jan J., Luijten, Peter, Sleijpen, Gerard L. G., van den Berg, Cornelis A. T.

“…Designing multidimensional radiofrequency pulses for clinical application must take into account the local specific absorption rate (SAR) as controlling the…”
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An overview of approaches for the stable computation of hybrid BiCG methods by Sleijpen, Gerard L.G., van der Vorst, Henk A.

“…It is well known that BiCG can be adapted so that the operations with A T can be avoided, and hybrid methods with computational complexity almost similar to…”
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Solving linear equations with a stabilized GPBiCG method by Abe, Kuniyoshi, Sleijpen, Gerard L.G.

“…Any residual polynomial of hybrid Bi-Conjugate Gradient (Bi-CG) methods, as Bi-CG STABilized (Bi-CGSTAB), BiCGstab(ℓ), Generalized Product-type Bi-CG (GPBiCG),…”
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Bi-CGSTAB as an induced dimension reduction method by Sleijpen, Gerard L.G., Sonneveld, Peter, van Gijzen, Martin B.

“…The Induced Dimension Reduction method [P. Wesseling, P. Sonneveld, Numerical experiments with a multiple grid- and a preconditioned Lanczos type method, in:…”
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Time efficient design of multi dimensional RF pulses: Application of a multi shift CGLS algorithm by Sbrizzi, Alessandro, Hoogduin, Hans, Lagendijk, Jan J., Luijten, Peter, Sleijpen, Gerard L. G., van den Berg, Cornelis A. T.

“…Designing multi dimensional ratio frequency excitation pulses in the small flip angle regime commonly reduces to the solution of a least squares problem, which…”
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BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices by Abe, Kuniyoshi, Sleijpen, Gerard L.G.

“…We propose Bi-Conjugate Residual (BiCR) variants of the hybrid Bi-Conjugate Gradient (BiCG) methods (referred to as the hybrid BiCR variants) for solving…”
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Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems by van Gijzen, Martin B., Sleijpen, Gerard L. G., Zemke, Jens-Peter M.

“…SUMMARYWe give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi‐shift…”
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Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem by Hochstenbach, Michiel E., Sleijpen, Gerard L. G.

“…After reviewing the harmonic Rayleigh–Ritz approach for the standard and generalized eigenvalue problem, we discuss several extraction processes for subspace…”
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A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems by Gerard L. G. Sleijpen, Van der Vorst, Henk A.

“…In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated…”
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Two-sided and alternating Jacobi–Davidson by Hochstenbach, Michiel E., Sleijpen, Gerard L.G.

“…We discuss two variants of a two-sided Jacobi–Davidson (JD) method, which have asymptotically cubic convergence for nonnormal matrices, and aim to find both…”
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Accurate conjugate gradient methods for families of shifted systems by van den Eshof, Jasper, Sleijpen, Gerard L.G.

“…We consider the solution of the linear system A T A +σ I x σ= A T b , for various real values of σ. This family of shifted systems arises, for example, in…”
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Relaxation strategies for nested Krylov methods by van den Eshof, Jasper, Sleijpen, Gerard L.G., van Gijzen, Martin B.

“…This paper studies computational aspects of Krylov methods for solving linear systems where the matrix–vector products dominate the cost of the solution…”
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Numerical solution of the two-dimensional Poincaré equation by Swart, Arno, Sleijpen, Gerard L.G., Maas, Leo R.M., Brandts, Jan

“…This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers…”
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Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems by Sleijpen, Gerard L. G., Booten, Albert G. L., Fokkema, Diederik R., van der Vorst, Henk A.

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Optimal a priori error bounds for the Rayleigh-Ritz method by SLEIJPEN, Gerard L. G, VAN DEN ESHOF, Jasper, SMIT, Paul

“…We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of…”
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Maintaining convergence properties of BiCGstab methods in finite precision arithmetic by Sleijpen, Gerard L. G., van der Vorst, Henk A.

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Alternative correction equations in the Jacobi-Davidson method by Genseberger, Menno, Sleijpen, Gerard L. G.

“…The correction equation in the Jacobi‐Davidson method is effective in a subspace orthogonal to the current eigenvector approximation, whereas for the…”
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Generalized conjugate gradient squared by Fokkema, Diederik R., Sleijpen, Gerard L.G., Van der Vorst, Henk A.

“…The Conjugate Gradient Squared (CGS) is an iterative method for solving nonsymmetric linear systems of equations. However, during the iteration large residual…”
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