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".
>
> lnk?


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;-)
> http://en.wikipedia.org/wiki/Krylov_subspace


I don't trust Wiki

> I like this books:
> http://www-users.cs.umn.edu/~saad/books.html


ok thanks

--
Rich