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 recursive divide and conquer algorithm to compute the inverse of an unreduced tridiagonal matrix based on the recursive application of the Sherman?Morrison formula to a diagonally dominant tridi diagonal matrix to avoid numerical stability problems is discussed.
2 citations
Posted Content•
TL;DR: In this article, a trigonometric cubic B-spline collocation method was used to solve the Coupled Burgers equation in time by using the Crank-Nicolson method.
Abstract: The coupled Burgers equation is solved by way of the trigonometric B-spline collocation method. The unknown of the coupled Burgers equation is integrated in time by aid of the Crank-Nicolson method. Resulting time-integrated coupled Burgers equation is discretized using the trigonometric cubic B-spline collocation method. Fully-integrated couupled Burgers equation which is a system of nonlinear algebraic equation is solved with a variant of Thomas algorithm. The three model test problems are studied to illustrate the accuracy of the suggested method.
2 citations
Journal Article•
TL;DR: This work analyzes and develops on effective algorithm for tridiagonal matrix pencils by removing the principal difficulty encoutered by Wilkinison (1958), which leads to the twisted factorisation of Henrici (1963) and also to a measure of singularity which was known to Babuska (1972) in a different context.
2 citations
TL;DR: A new direct method called the recursive tri-reduction method is developed for the tridiagonal system, which has the advantage over the Gaussian Elimination procedure when the authors use the parallel computer.
Abstract: Systems of tridiagonal equations frequently arise in practical applications related to solving ordinary or partial differential equations by discrete numerical methods. In this paper a new direct method called the recursive tri-reduction method is developed for the tridiagonal system. The method is simple and has the advantage over the Gaussian Elimination procedure when we use the parallel computer.
2 citations
1 Jan 2013
TL;DR: It is shown that the principle of the linear interpolation method and double parameter method is consistent and it points out that in this principle, the solutions to certain types of tridiagonal equations in the two methods are not stable.
Abstract: Based on the analysis of the two kinds of algorithms in solving large-scale tridiagonal linear equations, which are linear interpolation method and the method of double parameters, it is shown that the principle of the linear interpolation method and double parameter method is consistent and it points out that in this principle, the solutions to certain types of tridiagonal equations in the two methods are not stable. But in the case of not so sick, their relative errors of solution are very small, and the situation is very stable.
2 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |