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