Topic
Tridiagonal matrix algorithm
About: Tridiagonal matrix algorithm is a research topic. Over the lifetime, 1070 publications have been published within this topic receiving 21084 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: For every real square matrix A there exists a nonsingular real matrix X, for which X − 1 AX is a tridiagonal matrix, and under certain conditions X is uniquely determined.
Abstract: For every real square matrix A there exists a nonsingular real matrix X, for which X −1 AX is a tridiagonal matrix, and under certain conditions X is uniquely determined. Simple proofs are presented for the existence and uniqueness of this transformation.
5 citations
TL;DR: A symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns and derived by using partition together with UL factorization is presented.
Abstract: In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.
5 citations
TL;DR: In this paper, the Schrodinger equation with the Eckart potential is studied in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator.
Abstract: The Schrodinger equation with the Eckart potential is studied in this paper by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation and the wavefunctions are expressed in terms of the Jocobi polynomial.
5 citations
TL;DR: Two exact algorithms are proposed to solve the steady state probability distributions of irreducible Markov chains whose generator matrices have tridiagonal structure based on divide-and-conquer procedure and a parallel algorithm.
5 citations
TL;DR: In this article, an asymptotic fitted approach is presented to solve singularly perturbed delay differential equations of second order with left and right boundary. But the applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.
Abstract: In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation; O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.
5 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |