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

Authors

  • Debnath S Department of Computer Science, JIS College of Engineering, Kalyani, Nadia, India
  • Nath I Department of Computer Science, JIS College of Engineering, Kalyani, Nadia, India
  • Singh D Department of Computer Science, JIS College of Engineering, Kalyani, Nadia, India

Keywords:

matrix, multiplication, complexity, array

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.

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.

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Published

2025-11-26

How to Cite

[1]
S. Debnath, I. Nath, and D. Singh, “A New Heuris tic for Multiplication of two matrices of order 2*2”, Int. J. Comp. Sci. Eng., vol. 7, no. 18, pp. 44–47, Nov. 2025.

Issue

Vol. 7 No. 18 (2019): IJCSE Special Issue May Edition

Section

Research Article

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