A Symbolic Algorithm for Solving Doubly Bordered k-Tridiagonal Interval Linear Systems

Abstract

Doubly bordered k-tridiagonal interval linear systems play a crucial role in various mathematical and engineering applications where uncertainty is inherent in the system’s parameters. In this paper, we propose a novel symbolic algorithm for solving such systems efficiently. Our approach combines symbolic computation techniques with interval arithmetic to provide rigorous solutions in the form of tight interval enclosures. By exploiting the tridiagonal structure and employing a divide-and-conquer strategy, our algorithm achieves significantly reduced computational complexity compared to existing numerical methods. We also present theoretical analysis and provide numerical experiments to demonstrate the effectiveness and accuracy of our algorithm. The proposed symbolic algorithm offers a valuable tool for handling doubly bordered k-tridiagonal interval linear systems and opens up possibilities for addressing uncertainty in real-world problems with improved efficiency and reliability.