# 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)

## Arguments

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

## See also

*Version 2.7, authors: Ilya Kuprov*