Data for 'Fast Matrix Operations in Computer Algebra'

Data for 'Fast Matrix Operations in Computer Algebra'

This data package contains Maple worksheets with code executing algorithms pertaining to fraction-free Bunch-Hopcroft matrix inversion. The worksheets also include timing procedures used to obtain a log-log plot to describe the experimental asymptotic behaviour of the run time of the new fraction free algorithm. The plot and corresponding raw data are also included in the package. More information about these algorithms is available from the corresponding papers, 'Fast Matrix Operations in Computer Algebra' and 'On Fast Matrix Inversion'.

Cite this dataset as:
Tonks, Z., 2017. Data for 'Fast Matrix Operations in Computer Algebra'. University of Bath. https://doi.org/10.15125/BATH-00460.

Export

Data

logplotBH.png
image/png (23kB)
Creative Commons: Attribution 4.0

%27Fast_Matrix_ ... g_Procedures.mw
application/xml (47kB)
Software: MIT License

%27On_Fast_Matr ... g_Procedures.mw
application/xml (39kB)
Software: MIT License

%27Fast_Matrix_ ... rimentation.csv
text/plain (859B)
Creative Commons: Attribution 4.0

Creators

Zak Tonks
University of Bath

Contributors

James Davenport
Editor
University of Bath

Gregory Sankaran
Editor
University of Bath

University of Bath
Rights Holder

Coverage

Collection date(s):

From 1 June 2016 to 5 December 2017

Documentation

Data collection method:

The code was written at the University of Bath by Zak Tonks. "Fraction-Free Bunch-Hopcroft" is an adaptation of Bunch-Hopcroft matrix inversion as per references. The other algorithms used are as per references. Such code was written in Maple courtesy of Maplesoft. The experimental timing data was obtained using code from the worksheets by Zak Tonks, in Maple 2016. The CodeTools package in Maple was used to obtain CPU times for computations.

Data processing and preparation activities:

The timing data were formatted in a log-log plot in Maple by Zak Tonks.

Technical details and requirements:

The experimentation was originally performed in Maple 2016, using the version of CodeTools packaged with it. The current worksheets were saved in Maple 2017. The specification of the computer used for experimentation is as follows: - Intel Micro ATX DQ67SW - Intel Core I5 -2500 3.33GHz - 16GB RAM

Additional information:

'On Fast Matrix Inversion' is an extension paper detailing further developments on 'Fast Matrix Operations in Computer Algebra'. 'On Fast Matrix Inversion'...mw and 'Fast Matrix Operations...'...mw detail algorithms as per each paper respectively. In particular, a newer fraction-free Bunch-Hopcroft algorithm is presented in the former worksheet. Original algorithm for "Strassen-Winograd" (referred to as Strassen in worksheets and Winograd in 'Fast-Matrix Operations in Computer Algebra') can be found at [3]. Original algorithm for "Bunch-Hopcroft" can be found at [2]. Original Strassen's algorithm at [1]. "Fraction-Free Bunch-Hopcroft" an adaptation of [2]. References: [1] V. Strassen, “Gaussian Elimination is not Optimal,” Numer. Math., vol. 13, pp. 354–356, 1969. [2] J. Bunch and J. Hopcroft, “Triangular factorization and inversion by fast matrix multiplication,” Mathematics of Computation, vol. 28, pp. 231–236, 1974. [3] S. Winograd, “On multiplication of 2 x 2 matrices,” Linearalgebra and its applications, vol. 4, pp. 381–388, 1971.

Funders

Undergraduate Final Year Project

Engineering and Physical Sciences Research Council (EPSRC)
https://doi.org/10.13039/501100000266

PhD Studentship
EP/EG-CM1146/1

Bath Institute for Mathematical Innovation

Undergraduate Research Internship

Maplesoft

PhD Studentship
EP/EG-CM1146/1

Publication details

Publication date: 13 December 2017
by: University of Bath

Version: 1

DOI: https://doi.org/10.15125/BATH-00460

URL for this record: https://researchdata.bath.ac.uk/id/eprint/460

Contact information

Please contact the Research Data Service in the first instance for all matters concerning this item.

Contact person: Zak Tonks

Departments:

Faculty of Science
Computer Science
Mathematical Sciences