Date: Oct 18, 2013 6:06 PM
Author: Rich Delaney
Subject: Re: Krylov
On October 14, 2013, bartekltg wrote:
> > I saw an article, "the top 10 algorithms for the 21st century".
Computers in science and engineering, Jan. 2000
> > One of these was Krylov subspaces.
> > Can anyone clue me in what this is, and what for? Not
> > looking for a math seminar, more like apps. And why
> > is the algorithm, whatever it does, so important?
> This is family of numerical algorithms.
> Mostly solving linear systems (Preconditioned Conjugate Gradient[!],
> GMRES) and eigenvalue problems (Arnoldi, Lanczos).
> Every time you use a iterative methods for sparse linear system
> it probably use one of krylov methods.
> Why important? They have better convergence.
> "Classical" (Jacobi, SOR) iterative methods converge
> like ((1-x)/(1+x))^n,
> while krylov converge like ((1-sqrt(x))/(1+sqrt(x)))^n
> x = cond(A) - spectral condition number of matrix/operator A.
> > If I wanted to research this further, would it be
> > a linear algebra book, or numerical analysis, or what?
> Rather numerical analysis.
> BTW. Wiki is good start;-)
I don't trust Wiki
> I like this books: