Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

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. 

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

The k-tridiagonal matrices have received much attention in recent years. Many different algorithms have been proposed to improve the efficiency of k-tridiagonal matrix estimation. A novel method based on interval analysis has been identified to improve the efficiency of the calculation. This paper presents efficient and reliable computational algorithms for determining the determinant and inverse of general k-tridiagonal interval matrices built on generalized interval arithmetic. This study is based on the Doolittle LU factorization of the interval matrix. Finally, examples are presented to illustrate the algorithms.

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

pdf/implementing-interval-linear-equations-systems-for-enhanced-4h1gtm8a7r.pdf

Implementing Interval Linear Equations Systems for Enhanced Circuit Analysis

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Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Implementing Interval Linear Equations Systems for Enhanced Circuit Analysis

Tridiagonal Interval Matrix: Exploring New Perspectives and Application