arnoldi.m

Arnoldi procedure for the creation of an orthonormal Krylov basis from repeated action by an operator on a vector. The procedure is numerically unstable and must be used with caution.

Syntax

    [V,H]=arnoldi(Op,v0,niter)

Parameters

   Op     - function handle taking in a column vector 
            and returning another column vector

   v0     - starting vector of the Arnoldi process

   nsteps - number of iterations to take; the Krylov
            subspace will be nsteps+1 dimensional

Outputs

   V - a matrix containing the orthonormal basis vec-
       tors of the Krylov subspace in columns

   H - extended Hessenberg matrix

Notes

If exact Krylov breakdown occurs, V and H are truncated to the completed invariant subspace.

See also

acomm.m, atranspose.m, aux_mat.m, binpack.m, cheap_norm.m, cheb_coeff.m, clean_up.m, dirdiff.m, eigenfields.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, fourdif.m, fourlap.m, frob_chop.m, gaussfun.m, hdot.m, herm_spline.m, jacobianest.m, keep_rank.m, krondelta.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, remncomm.m, remtrace.m, rspert.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, tikhonov.m, trapdiff.m, unit_oper.m, unit_state.m, vvpert.m, Kernel_utilities

Version 2.7, authors: Ilya Kuprov