Computing the square root of a low-rank perturbation of the scaled identity matrix

About

The MATLAB code in this repository was used to produce the figures and tables in sections [sect. 1, 1] and [sect. 5, 1]. The results in the manuscript were produced by running these codes in MATLAB 2021b on a machine equipped with an AMD Ryzen 7 PRO 5850U and 32 GiB of RAM.

Dependencies

The code leverages the capabilities of the Advanpix Multiprecision Computing Toolbox for MATLAB [3] to compute residual and forward error in higher-than-working precision.

Running the tests

The run_tests script sets up the test environment and runs the test suite. Our code is organized in three folders:

• data, which contains the matrices provided as part of the Lingvo Framework [2] for TensorFlow in .mat format;
• include, which contains utility functions for computing the residual and forward error, for formatting numbers as LaTeX strings, and for timing the execution of MATLAB functions;
• methods, which contains our implementation of the algorithms for computing the square root of low-rank perturbations of the scaled identity; and
• tests, which contains the functions that run the algorithms, compute the execution time, residual, and forward error, and store the results to file.

References

[1] M. Fasi, N. J. Higham, and X. Liu. Computing the square root of a low-rank perturbation of the scaled identity matrix. MIMS EPrint 2021.X, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, December 2021.

[2] Lingvo.

[3] Multiprecision Computing Toolbox for MATLAB. Advanpix LLC. Yokohama, Japan.

If you use the code in this repository, please cite the preprint [1].

License

This software is distributed under the terms of the BSD 2-Clause "Simplified" license (see LICENSE.md).