Черната скала, Боровец, България, 2021

A light-weight MATLAB package for prototyping low-synchronization block Arnoldi methods with generalized inner products. The primary aim of this project is to benchmark speed, accuracy, and stability of multiple configurations of such methods. There are four main axes required to specify an algorithm configuration:

  • inner product: choice of block inner product

  • skeleton: the inter-orthongalization routine applied between block vectors

  • muscle: the intra-orthogonalization routine applied to an individual block vector

  • modification: whether to use vanilla FOM (Full Orthogonalization Method), or a modified version, like GMRES.

Associated work:

A lean MATLAB package for exploring stability properties of block Gram-Schmidt and block GMRES variations.

Associated work:

Ecublens, Vaud, CH, 2018

This repository contains the MATLAB code written for

The syntax is based off B(FOM)^2, and the scripts allow one to reproduce the same results shown in the paper.

Versailles, France, 2009
Versailles, FR, 2009

Written in MATLAB and used in my thesis and the following papers:

The package comprises implementations of the classical, global, loop-interchange, and hybrid BFOM and B(FOM)^2, written in a modular fashion so that users can easily switch between choices of block inner products and scaling quotients. It also contains thorough documentation and the scripts to generate the examples in the papers. All data matrices have been moved to Zenodo, and the code contains scripts to download them automatically.