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