Data for 'Fast Matrix Operations in Computer Algebra'

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.