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: A parallel algorithm for the solution of the general tridiagonal system is presented, based on an efficient implementation of Cramer's rule, in which the only divisions are by the determinant of the matrix.
Abstract: . A parallel algorithm for the solution of the general tridiagonal system is presented. The method is based on an efficient implementation of Cramer's rule, in which the only divisions are by the determinant of the matrix. Therefore, the algorithm is defined without pivoting for any nonsingular system. 0(n) storage is required for n equations and 0(log n) operations are required on a parallel computer with n processors. 0(n) operations are required on a sequential computer. Experimental results are presented from both the CDC 7600 and CRAY-1 computers.
38 citations
38 citations
1 Jan 2007
TL;DR: The new representation for the inverse of block tridiagonal and banded matrices is shown to be numerically stable over a variety of blocktridiagonal matrices and to be more computationally efficient than the previously proposed techniques.
Abstract: We provide a new representation for the inverse of block tridiagonal and banded matrices. The new representation is shown to be numerically stable over a variety of block tridiagonal matrices, in addition of being more computationally efficient than the previously proposed techniques. We provide two algorithms for commonly encountered problems that illustrate the usefulness of the results.
37 citations
TL;DR: The exponential cubic B-spline algorithm is presented to find the numerical solutions of the Korteweg-de Vries (KdV) equation, which is solved by using a variant of Thomas algorithm.
Abstract: The exponential cubic B-spline algorithm is presented to find the numerical solutions of the Korteweg-de Vries (KdV) equation. The problem is reduced to a system of algebraic equations, which is solved by using a variant of Thomas algorithm. Numerical experiments are carried out to demonstrate the efficiency of the suggested algorithm.
37 citations
TL;DR: In this paper, the authors use the theory of orthogonal polynomials to write down explicit expressions for the polynomial of the first and second kind associated with a given infinite symmetric tridagonal matrix H-zI.
Abstract: We use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal matrix H. The Green's function is the inverse of the infinite symmetric tridiagonal matrix (H-zI). By calculating the inverse of the finite symmetric tridiagonal matrix we can find the analytical form of the inverse of the finite symmetric tridiagonal matrix, .
37 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |