Block Gram-Schmidt
and related Krylov subspace algorithms
A lean MATLAB package for exploring stability properties of block Gram-Schmidt variations.
Associated publications:
Erin C. Carson, Kathryn Lund, Yuxin Ma, and Eda Oktay. Reorthogonalized Pythagorean variants of block classical Gram-Schmidt, In preparation, 2024.
Erin C. Carson, Kathryn Lund, Miroslav Rozložník, and Stephan Thomas: Block Gram-Schmidt algorithms and their stability properties, Linear Algebra and its Applications, Vol. 628, pp. 150-195, 2022.
Erin C. Carson, Kathryn Lund, and Miroslav Rozložník: The stability of block variants of classical Gram-Schmidt. SIAM Journal on Matrix Analysis and Applications, 42(3), pp. 1365--1380, 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 publications:
Kathryn Lund. Adaptively restarted block Krylov subspace methods with low-synchronization skeletons. Numerical Algorithms, Vol. 93, 731--764, 2023.