New Symbolic Algorithms For Solving A General Bordered Tridiagonal Linear System
A. A. Karawia
TL;DR
This paper introduces two reliable symbolic algorithms for solving general bordered tridiagonal linear systems, utilizing LU decomposition and Sherman-Morrison-Woodbury formula, with implementations demonstrated in CAS like MAPLE, MATLAB, and MATHEMATICA.
Contribution
It presents novel symbolic algorithms specifically designed for bordered tridiagonal systems, improving computational efficiency and implementation in computer algebra systems.
Findings
Algorithms successfully solve bordered tridiagonal systems
Implementation in CAS demonstrates practicality
Computational cost is O(n) for the LU-based method
Abstract
In this paper, the author present reliable symbolic algorithms for solving a general bordered tridiagonal linear system. The first algorithm is based on the LU decomposition of the coefficient matrix and the computational cost of it is O(n). The second is based on The Sherman-Morrison-Woodbury formula. The algorithms are implementable to the Computer Algebra System (CAS) such as MAPLE, MATLAB and MATHEMATICA. Three examples are presented for the sake of illustration.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Numerical Methods and Algorithms