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A Method To Calculate Determinants, With Computer Algorithm Interpretation
[Full Text]
AUTHOR(S)
Armend Salihu, Fatlinda Salihu
KEYWORDS
Determinants, computer agorithm, determinant calculation, time comparison.
ABSTRACT
In this paper we present the new algorithm to calculate determinants of nth order using Rezaifar's method of reducing the order of determinants to second order. We have implemented the Dodgson's algorithm within Rezaifar's method to calculate sub matrices and developed a new method. Within the paper we have also developed the computer algorithm to calculate the determinant using this new method. While comparing the computer execution time with the Rezaifar's method, we have seen that this new algorithm presented is executed faster.
REFERENCES
A. Salihu, “A method to compute the determinant of square matrices of order five and six”, Open Journal of Mathematical Science, 3, pp. 84-93, 2019.
C. L. Dodgson, “Condensation of Determinants, Being a New and Brief Method for Computing their Arithmetic Values”, Proc. Roy. Soc. Ser. A, 15, pp. 150-155, 1866.
R. Farhadian, “On A Method to Compute the Determinant of Square Matrices of Order Four”, International Journal of Scientific and Innovative Mathematical Research, 5, p.5, 2017.
R. Farhadian, “A Method to Compute the Determinant of 5×5 Matrix”, Open Journal of Mathematical Science, 2, pp. 156-163, 2018.
J. Kiusalaas, “Numerical Methods in Engineering with MATLAB”, Cambridge University Press, Cambridge, 2005.
O. Rezaifar and H. Rezaee, “A new approach for finding the determinant of matrices”, Applied Mathematics and Computation, 188, pp. 1445-1454, 2007.
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