f(A)b
f(A)b
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A toolbox, survey, test problem collection, and much more aimed at addressing goals outlined by the 2023 f(A)bulous Workshop. Currently under development.
Associated publications:
Massimiliano Fasi, Stéphane Gaudreault, Kathryn Lund, and Marcel Schweitzer. Challenges in computing matrix functions. arXiv:2401.16132, 2024.
A MATLAB toolbox for computing the Fréchet derivative of the tensor t-function. Third-order tensors are encoded as structs, with fields storing the dimensions and the unfolded tensor configuration. As opposed to built-in multidimensional arrays in MATLAB, our "tensor structs" allow for sparse storage and operations. The syntax is built off LowSyncBlockArnoldi and bfomfom and allows for general matrix-function solver configurations, e.g., choice of underlying inner product, norm, (block) Arnoldi implementation, etc.
Associated publications:
Kathryn Lund and Marcel Schweitzer. The Fréchet derivative of the tensor t-function. Calcolo, Vol 60(35), 2023.
Magdeburg, DE, 2022
Versailles, FR, 2009
Written in MATLAB and used in my thesis and the following papers:
Andreas Frommer, Kathryn Lund, and Daniel B. Szyld, Block Krylov subspace methods for functions of matrices II: Modified block FOM, SIAM Journal on Matrix Analysis and Applications, 41(2), pp. 804--837, 2020. Data matrices on Zenodo.
Kathryn Lund, The tensor t-function: a definition for functions of third-order tensors, Numerical Linear Algebra with Applications, 27 (3), e2288, 2020. Data matrices on Zenodo.
Andreas Frommer, Kathryn Lund, and Daniel B. Szyld, Block Krylov subspace methods for functions of matrices, Electronic Transactions on Numerical Analysis, Vol. 47, pp. 100--126, 2017. Data matrices on Zenodo.
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.
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