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A New Heuris tic for Multiplication of two matrices of order 2*2

Shankar Debnath1 , Ira Nath2 , Dharmpal Singh3

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-18 , Page no. 44-47, May-2019

Online published on May 25, 2019

Copyright © Shankar Debnath, Ira Nath, Dharmpal Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: Shankar Debnath, Ira Nath, Dharmpal Singh, “A New Heuris tic for Multiplication of two matrices of order 2*2,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.18, pp.44-47, 2019.

MLA Style Citation: Shankar Debnath, Ira Nath, Dharmpal Singh "A New Heuris tic for Multiplication of two matrices of order 2*2." International Journal of Computer Sciences and Engineering 07.18 (2019): 44-47.

APA Style Citation: Shankar Debnath, Ira Nath, Dharmpal Singh, (2019). A New Heuris tic for Multiplication of two matrices of order 2*2. International Journal of Computer Sciences and Engineering, 07(18), 44-47.

BibTex Style Citation:
@article{Debnath_2019,
author = {Shankar Debnath, Ira Nath, Dharmpal Singh},
title = {A New Heuris tic for Multiplication of two matrices of order 2*2},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {5 2019},
volume = {07},
Issue = {18},
month = {5},
year = {2019},
issn = {2347-2693},
pages = {44-47},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=1332},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=1332
TI - A New Heuris tic for Multiplication of two matrices of order 2*2
T2 - International Journal of Computer Sciences and Engineering
AU - Shankar Debnath, Ira Nath, Dharmpal Singh
PY - 2019
DA - 2019/05/25
PB - IJCSE, Indore, INDIA
SP - 44-47
IS - 18
VL - 07
SN - 2347-2693
ER -

           

Abstract

From the very beginning of computer era, the scientists are trying their best for searching the method which can reduce the complexity of multiplication of matrices. In case of ordinary matrix multiplication of two given 2*2 matrixes, we use three for loops to determine the product of these two matrixes and produce a resultant two-dimensional matrix. Then the complexity of the algorithm is n3. Although this problem has been studying extensively, we intend to implement and modify the pre-existing procedure. So, we decide to tackle the multiplication of those two two-dimentional matrixes by using a one-dimensional array. The algorithm that we develop will store all the elements of two 2x2 matrixes in a single one-dimensional array. Then we generalized a formula that will provide the co-relationship between the index number of the one-dimensional array to find the product of those two 2*2 matrixes. So, in our case we determine the result by using two for loops only that basically reduce the complexity.

Key-Words / Index Term

matrix,multiplication,complexity, array

References

[1] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, “Introduction to Algorithms”, the MIT Press.
[2] Aho, A.V., Hopcroft, J.E., and Ullman, J.D,”The Design and Analysis of Computer Algorithms”. Addison-Wesley, Reading,,MA, 1974.
[3] Khaled Thabet, Sumaia AL-Ghuribi , “Matrix Multiplication Algorithms”, IJCSNS International Journal of Computer Science and Network Security, VOL.12 No.2, February 2012.
[4] IVO HEDTKE,” STRASSEN’S MATRIX MULTIPLICATION ALGORITHM FOR MATRICES OF ARBITRARY ORDER”, Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 2(2011), Pages 269-277.