论文信息 - GMRES and Integral Operators

GMRES and Integral Operators

In this paper we show how the properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates by an implicit application of Nystrom interpolation, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden’s method. We present an example to illustrate the ideas.

C. T. Kelley | Z. Q. Xue

[1] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2] J. J. Moré,et al. On the Global Convergence of Broyden''s Method , 1974 .

[3] Gilbert Strang,et al. The application of quasi‐Newton methods in fluid mechanics , 1981 .

[4] Jorge Nocedal,et al. Theory of algorithms for unconstrained optimization , 1992, Acta Numerica.

[5] D. Gay,et al. Some Convergence Properties of Broyden&Apos;S Method , 1977 .

[6] Lloyd N. Trefethen,et al. How Fast are Nonsymmetric Matrix Iterations? , 1992, SIAM J. Matrix Anal. Appl..

[7] D. M. Hwang,et al. Convergence of Broyden's Method in Banach Spaces , 1991, SIAM J. Optim..

[8] I. Duff,et al. The state of the art in numerical analysis , 1997 .

[9] Jorge Nocedal,et al. Representations of quasi-Newton matrices and their use in limited memory methods , 1994, Math. Program..

[10] O. Nevanlinna. Convergence of Iterations for Linear Equations , 1993 .