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
26 Aug 1996
TL;DR: The 2-steps graph which occurs in the parallelization of Gaussian elimination with partial pivoting is presented and an optimal parallel algorithm with two processors is presented.
Abstract: This paper presents the 2-steps graph which occurs in the parallelization of Gaussian elimination with partial pivoting. We compute the task deadlines and the lower bound of processors popt (n) for executing the task graph in minimal time (n is the size of the considered matrix). Finally, we present an optimal parallel algorithm with two processors.
Posted Content•
TL;DR: In this article, the transmittance through a quantum wire connected with two electron reservoirs is calculated and non-trivial transformation between the evolution operator method and the Green's function technique is reported.
Abstract: In this paper the transmittance through a quantum wire connected with two electron reservoirs is calculated and non-trivial transformation between the evolution operator method and the Green's function technique is reported. To show this equivalence an analytical nonlinear formula which concerns symmetrical tridiagonal matrices is proofed. This formula connects the cofactor and three determinants of tridiagonal matrices.
1 Jan 2015
TL;DR: Some tests are reported on the performance of the parallelized solver, which shows the spike algorithm is expected to provide an efficient solver on modern multicore machines.
Abstract: 2015/1/9 2 We are developing a recursive direct-solver for linear equations with the coefficient matrix of a tridiagonal block form by adopting the spike algorithm. The solver is parallelized by open MP that supports sections and task constructs. The block structure in the coefficient matrix naturally leads to nested parallelism. Some tests are reported on the performance of the parallelized solver, which shows the spike algorithm is expected to provide an efficient solver on modern multicore machines.
TL;DR: A new algorithm, the double-bordering algorithm, for the solution of linear systems of equations is derived, and its complexity is shown to be compatible with the complexity of Gaussian elimination.
Abstract: A new algorithm, the double-bordering algorithm, for the solution of linear systems of equations is derived, and its complexity is shown to be compatible with the complexity of Gaussian elimination, The application of the algorithm to the solution of block-tridiagonal systems is also described
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |