W dniu 2013-10-14 23:12, firstname.lastname@example.org 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.
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?