R. Sidje and A. Williams. Fast generalised cross validation. In International Linear Algebra Year:Linear Algebra in Optimization. CERFACS, Albi-Toulouse, France, 1996. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
On the performance of various adaptive preconditioned GMRES.. - Burrage (1997) (1 citation) (Correct)
....deflating of a small number of eigenvalues gives little advantage over restarted GMRES. However, in this GCV application a number of systems of equations have to be solved which are just updated by a constant diagonal term . By preserving the eigenvectors across the systems, as shown in [20] and [16], deflation can work very impressively across systems of equations if special structures can be exploited (in this case the eigenvectors remain the same from system to system) Problem 5 Problem 3 gives an example where MORGAN(k,m) is efficient for a large linear system. Finally, we report ....
R. Sidje and A. Williams. Fast generalised cross validation. In International Linear Algebra Year:Linear Algebra in Optimization. CERFACS, Albi-Toulouse, France, 1996.
An augmented subspace Conjugate Gradient - Erhel, al (1997) (Correct)
....a sequence of linear systems of the form (A oe (i) I)x (i) b with the same right hand side. In this case, the Krylov subspace generated by a Lanczos method is the same for any system and it can be used very efficiently along with recurrences to compute the quantities required by GCV [11, 21]. Here we assume that the different right hand sides b (i) are computed sequentially. This situation arises for instance when a new right hand side depends upon previous solutions. A first idea is to use previous systems to derive an initial guess for the current system. In [10] the current ....
R. Sidje and A. Williams, Fast generalised cross validation, in International Linear Algebra Year:Linear Algebra in Optimization, CERFACS, Albi-Toulouse, France, 1996.
An augmented subspace Conjugate Gradient - Erhel, Guyomarc'h (1997) (Correct)
....a sequence of linear systems of the form (A oe (i) I)x (i) b with the same right hand side. In this case, the Krylov subspace generated by a Lanczos method is the same for any system and it can be used very eOEciently along with recurrences to compute the quantities required by GCV [11, 21]. Here we assume that the dioeerent right hand sides b (i) are computed sequentially. This situation arises for instance when a new right hand side depends upon previous solutions. A rst idea is to use previous systems to derive an initial guess for the current system. In [10] the current ....
R. Sidje and A. Williams, Fast generalised cross validation, in International Linear Algebra Year:Linear Algebra in Optimization, CERFACS, Albi-Toulouse, France, 1996.
Generalized Cross-Validation for Large Scale Problems - Golub, von Matt (1996) (12 citations) (Correct)
.... V ( U 0 ( Note that mR ( Gamma1) u (m) n: However, since the numerator in L 0 ( is unbounded, we have lim #0 L 0 ( Gamma1; even though V ( 0. On the other hand U 0 ( remains bounded for # 0. The reader can find similar bounds on V 0 ( in Appendix C. In [30] R. Sidje and A. Williams consider the fitting of smoothing spline surfaces to meteorological data using GCV. They also use Hutchinson s trace estimator and the Lanczos algorithm to approximate the GCV function. However they do not take advantage of the theory of Gauss quadrature, and thus they ....
R. Sidje and A. Williams, Fast Generalised Cross Validation, SIAM J. Numer. Anal., submitted.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC