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: In this article, a solution for a problem on eigenvalues of some symmetric tridiagonal matrices suggested by William Trench is given for a generalization of the Trench problem.
109 citations
TL;DR: In this paper, an efficient and reliable technique has been developed to solve the large system of non-linear equations which describe the behaviour of multistage flash (MSF) desalination plants.
103 citations
7 Nov 1998
TL;DR: The main advantage of the new method over partial pivoting is that it permits a priori determination of data structures and communication pattern for Gaussian elimination, which makes it more scalable on distributed memory machines.
Abstract: We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is that it permits a priori determination of data structures and communication pattern for Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we design highly parallel algorithms for both sparse Gaussian elimination and triangular solve and we show that they are suitable for large-scale distributed memory machines.
101 citations
TL;DR: In this article, the quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto-Sivashinsky equation, and the accuracy of the proposed method is demonstrated by four test problems.
97 citations
TL;DR: In this paper, the exact solution for the resolvent matrix of a generalized tridiagonal Hamiltonian whose elements are themselves block matrices is obtained, and the capability of the method is demonstrated by applying it to study the electronic structure on the surface of semiconductors.
Abstract: The exact solution for the resolvent matrix of a generalized tridiagonal Hamiltonian whose elements are themselves block matrices is obtained. The capability of the method is demonstrated by applying it to study the electronic structure on the surface of semiconductors. Some interesting insights regarding the difference between the Shockley states and Tamm states are also discussed.
90 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |