A Hybrid Numerical Algorithm for Evaluating n-th Order Tridiagonal Determinants
Moawwad El-Mikkawy, and AbdelRahman Karawia
TL;DR
This paper introduces a new hybrid numerical algorithm that efficiently computes n-th order tridiagonal determinants in linear time without symbolic calculations, suitable for various programming languages.
Contribution
A novel hybrid numerical algorithm for evaluating general tridiagonal determinants in linear time, avoiding symbolic computations and applicable across multiple programming environments.
Findings
Algorithm operates in linear time
Avoids symbolic computation complexities
Demonstrates superior performance in tests
Abstract
The principal minors of a tridiagonal matrix satisfy two-term and three-term recurrences [1, 2]. Based on these facts, the current article presents a new efficient and reliable hybrid numerical algorithm for evaluating general n-th order tridiagonal determinants in linear time. The hybrid numerical algorithm avoid all symbolic computations. The algorithm is suited for implementation using computer languages such as FORTRAN, PASCAL, ALGOL, MAPLE, MACSYMA and MATHEMATICA. Some illustrative examples are given. Test results indicate the superiority of the hybrid numerical algorithm.
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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods for differential equations · Scientific Research and Discoveries