Matrices with tunable ∞-norm condition number and no need for pivoting in LU factorization

This repository contains the code for producing the data in the tables in [sect. 5, 1].

Dependencies

The code requires the GNU Scientific Library (GSL), the Intel Math Kernel Library (MKL), and OpenMPI.

Building the sources

Issuing make all should compile the source code and produce the two executables test_lowprec and test_norminf used in the experiments. The Makefile assumes that the code is being compiled on a Linux machine and that Intel MKL 2019 is available in the default location /opt/intel/compilers_and_libraries_2019. The variables CMAKE_PATH and CMAKE_INCLUDE in the Makefile should be modified to run the experiment on a system with a different configuration.

Running the experiments

The binary file test_lowprec is a standalone program and can be run with a simple ./test_lowprec. The binary file test_norminf should be used with the mpirun command, and the number of row and column processes to be used should be explicitly stated. The command

mpirun -n $(($nprows * $npcols)) ./test_norminf -m $nprows -n $npcols

should run to completion as long as the variables nprows and npcols are set and there are at least $(($nprows * $npcols)) available slots in the system (if not, the command line option --oversubscribe can be used).

References

If you use the code in this repository, please cite the preprint:

[1] M. Fasi and N. J. Higham. Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. MIMS EPrint 2020.17, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, July 2020.

License

This software is distributed under the terms of the GNU GPL v. 2 software license (see LICENSE.md).