Abstract
The main objective of this article is to make use of the induction variable elimination in the matrix multiplication task. The main obstacle to this aim is iterating through a matrix column, because it requires jumping over tables. As a solution to this trouble we propose a shifting window in a form of a table of auxiliary double pointers. The ready-to-use C++ source code is presented. Finally, we performed thorough time execution tests of the new C++ matrix multiplication algorithm. Those tests proved the high efficiency of the proposed optimization.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aceto, L.: Some applications of the Pascal matrix to the study of numerical methods for differential equations. Boll. del. Unione Matem. Ital. B 8(3), 639–651 (2005)
Aceto, L., Magherini, C., Weinmuller, E.B.: Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain. Appl. Math. Comp. 255, 179–188 (2015)
Augustyn, D.R., Warchal, L.: Cloud service solving N–body problem based on Windows Azure platform. Comm. in Comput. and Inf. Sci. 79, 84–95 (2010)
Augustyn, D.R.: Query-condition-aware histograms in selectivity estimation method. Adv. in Intel. and Soft Comput. 103, 437–446 (2011)
Bellman, R.: Introduction to Matrix Analysis. Society for Industrial Mathematics, New York (1987)
Coppersmith, Winograd S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9, 251–280 (1990)
Cormen, T.H., Leiserson, Ch.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd Edn. McGraw–Hill (2001)
Kernighan, B.W., Ritchie, D.M.: The C Programming Language. Prentice-Hall, New Jersey (1978)
Kincaid, D.R., Cheney, E.W.: Numerical Analysis: Mathematics of Scientific Computing, 3rd edn. Brooks Cole, California (2001)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1992)
Respondek, J.: On the confluent Vandermonde matrix calculation algorithm. Appl. Math. Lett. 24, 103–106 (2011)
Respondek, J.: Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices. Appl. Math. Comp. 218(5), 2044–2054 (2011)
Sakthivel, R., Ganesh, R., Anthoni, S.M.: Approximate controllability of fractional nonlinear differential inclusions. Appl. Math. and Comp. 225, 708–717 (2013)
Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13, 354–356 (1969)
Stroustrup, B.: The C++ Programming Language, 3rd edn. AT&T Labs, New Jersey (2000)
Stroustrup, B.: The Design and Evolution of C++, 9th edn. Addison-Wesley, Massachusetts (1994)
Waite, W.M., Goos, G.: Compiler Construction, Monographs in Computer Science, 2nd edn. Springer Verlag, New York (1983)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Respondek, J. (2015). Advanced Induction Variable Elimination for the Matrix Multiplication Task. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9155. Springer, Cham. https://doi.org/10.1007/978-3-319-21404-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-21404-7_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21403-0
Online ISBN: 978-3-319-21404-7
eBook Packages: Computer ScienceComputer Science (R0)