nidtec-una / krysbas-dev

A collection of Krylov Subspace-Based Adaptive Solvers (KrySBAS) written in MATLAB
https://krysbas-dev.readthedocs.io
GNU General Public License v3.0
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Encapsulate Arnoldi iteration #29

Closed jhabriel closed 11 months ago

jhabriel commented 11 months ago

Lines 280 -- 298 from pd_gmres should be encapsulated into:


[H, W] = modified_gram_schmidt_arnoldi(A, v, m)

% Inputs:
%
% A: matrix n-by-n
% v: normalised residual vector
% m: restart parameter
%
% Outputs:
% W: Orthonormal basis of Krylov subspace
% H: Upper Hessenberg matrix
%
gusespinola commented 11 months ago

https://en.wikipedia.org/wiki/Arnoldi_iteration

jhabriel commented 11 months ago

Note to self:

I just realised that the normalised residual vector v is used after the Arnoldi block. This means that we need to return it as an output.

We need to discuss how to incorporate this as part of the modified_gram_schmidt_arnoldi.