Development And Optimization Of A Deterministic Algorithm For Efficient Computation Of The Characteristic Polynomial Using K-Formulating Matrix Multiplication Techniques

Kushum Rani; Dr. Vinod Kumar

doi:10.69980/redvet.v25i1.1647

Kushum Rani
Dr. Vinod Kumar

DOI: https://doi.org/10.69980/redvet.v25i1.1647

Keywords: Deterministic Algorithm, Characteristic Polynomial, K-Formulating Matrix Multiplication, Computational Efficiency, Numerical Accuracy.

Abstract

This paper develops an optimized deterministic algorithm for computing characteristic polynomials for matrices with reasonable time complexity based on K-matrix multiplication matrix techniques. A novel algorithm with improved computational efficiency, from time complexity O(n4) down to O(n3), allows it to solve large matrices computationally efficiently. Experimental results of matrix sizes running from 10×10 up to 100×100, and comparison with existing methods, show substantial gains in computing time and memory use. The algorithm is highly accurate numerically for the three main classes of matrices: dense, sparse, and symmetric matrices. The obtained results here lead one to imagine a wide range of applications in scientific research, engineering, and data-intensive fields. The study demonstrates a robust and scalable solution for matrix-based computations, providing improvements in both efficiency and dependability.

Author Biographies

Kushum Rani

Research Scholar, Department of Mathematics, Om Sterling Global University, Hisar

Dr. Vinod Kumar

Research Supervisor, Department of Mathematics, Om Sterling Global University, Hisar

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