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Topic: Krylov
Replies: 2   Last Post: Oct 18, 2013 6:06 PM

 Messages: [ Previous | Next ]
 bartekltg Posts: 55 Registered: 12/11/12
Re: Krylov
Posted: Oct 14, 2013 7:25 PM

W dniu 2013-10-14 23:12, r_delaney2001@yahoo.com pisze:
> I saw an article, "the top 10 algorithms for the 21st century".

> 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).

I think most 'modern' methods.

@Apps?

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 like this books:

bartekltg

Date Subject Author
10/14/13 Rich Delaney
10/14/13 bartekltg
10/18/13 Rich Delaney