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'

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

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'

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