R. B. Morgan, Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations, SIAM Journal on Matrix Analysis and Applications, 21 (2000), pp. 1112--1135. Home/Search Document Not in Database Summary Related Articles Check |
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Analysis of Acceleration Strategies for Restarted.. - Eiermann, Ernst.. (2000) (4 citations) (Correct)
....process. We shall rer to such a procedure as deflation. Such problematic subspaces are often identified as eigenspaces of A associated with eigenvalues of small magnitude, but other spaces may sometimes be better suited. Examples of this approach are the augmentation method introduced by Morgan [23, 21] and analyzed by Saad [29, 30] and Chapman and Saad [2] Another device for eliminating U from the iteration is to introduce a preconditioner which inverts the orthogonal section of A onto U, as proposed by Erhel et al. 7] Baglama et al. 1] and, with certain modifications, by Kharchenko and ....
....Ritz vectors associated with the k harmonic Ritz values k of A with respect to the previous correction space which are closest to the origin. Since no eigenvector information is available in the first cycle, the first correction space is chosen as C = Km k (A; r 0 ) As shown by Morgan in [21], there is a less expensive implementation of this approach. Consider the MR approximation with initial residual r 0 with respect to the (m k) dimensional Krylov space Km k (A; r 0 ) As shown in Section 3.3, the associated residual vector has the representation m k (A)r 0 m k (i) ....
Ronald B. Morgan. Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations. to appear.
Analysis of Acceleration Strategies for Restarted.. - Eiermann, Ernst.. (2000) (4 citations) (Correct)
....process. We shall refer to such a procedure as de ation. Such problematic subspaces are often identi ed as eigenspaces of A associated with eigenvalues of small magnitude, but other spaces may sometimes be better suited. Examples of this approach are the augmentation method introduced by Morgan [15, 16] and analyzed by Saad [21, 22] and Chapman and Saad [2] Another device for eliminating U from the iteration is to introduce a preconditioner which inverts the orthogonal section of A onto U , as proposed by Erhel et al. 7] Baglama et al. 1] and, with certain modi cations, by Kharchenko and ....
....k harmonic Ritz values 1 ; k of A with respect to the previous correction space which are closest to the origin. Since no eigenvector information is available in the rst cycle, the rst correction space is chosen simply as C = Km k (A; r 0 ) As subsequently shown by Morgan in [16], there is a less expensive implementation of this approach. Consider the MR approximation with initial residual r 0 with respect to the (m k) dimensional Krylov space Km k (A; r 0 ) As shown in Section 3.3, the associated residual vector has the representation m k (A)r 0 ; where p m k ....
Ronald B. Morgan. Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations. SIAM J. Matrix Anal. Appl., 21(4):1112-1135, 2000.
Recycling Subspace Information for Diffuse Optical Tomography - Kilmer, de Sturler (2004) (Correct)
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R. B. Morgan, Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations, SIAM Journal on Matrix Analysis and Applications, 21 (2000), pp. 1112--1135.
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