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: The parallel-Thomas-algorithm (PTA) is developed and the solution of PTA is compared to two known parallel algorithms, i.e. cyclic-reduction (CR) and parallel-cyclic- reduction (PCR) and lid-driven cavity problem is considered to assess these parallel approaches.
Abstract: The solution of tridiagonal system of equations using graphic processing units (GPU) is assessed. The parallel-Thomas-algorithm (PTA) is developed and the solution of PTA is compared to two known parallel algorithms, i.e. cyclic-reduction (CR) and parallel-cyclic-reduction (PCR). Lid-driven cavity problem is considered to assess these parallel approaches. This problem is also simulated using the classic Thomas algorithm that runs on a central processing unit (CPU). Runtimes and physical parameters of the mentioned GPU and CPU algorithms are compared. The results show that the speedup of CR, PCR and PTA against the CPU runtime is 4.4x ,5.2x and 38.5x , respectively. Furthermore, the effect of coalesced and uncoalesced memory access to GPU global memory is examined for PTA, and a 2x -speedup is achieved for the coalesced memory access. Additionally, the PTA performance in a time dependent problem, the unsteady flow over a square, is assessed and a 9x-speedup is obtained against the CPU.
4 citations
1 Jun 2015
TL;DR: In this article, an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer, where a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh.
Abstract: In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that the proposed technique is of first order accurate and the error constant is independent of the perturbation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.
3 citations
Journal Article•
TL;DR: A new algorithm for inversing block periodic tridiagonal matrices is obtained, using the LU and UL decomposition of block tridiagon matrix and the special structure of its inversion, the Sheman-Morrison-Woodbury formula is used during this process.
Abstract: A new algorithm for inversing block periodic tridiagonal matrices is obtained,using the LU and UL decomposition of block tridiagonal matrix and the special structure of its inversion,the Sheman-Morrison-Woodbury formula is used during this process.Based on this algorithm,new algorithms for inversing periodic tridiagonal matrix and symmetric periodic tridiagonal matrix are also obtained.The computing complexity and the computing time of these algorithms are lower than the traditional algorithms.
3 citations
Journal Article•
TL;DR: In this paper, for inverse eigenproblems with given four eigenvalues and eigenvector, the authors considered necessary and sufficient conditions for the uniqueness of the solution, and provided a proof of the uniqueness.
Abstract: In this paper, for inverse eigenproblems with given four eigenvalues and eigenvector are considered and are given some necessary and sufficient conditions for the uniqueness of the solution.
3 citations
20 Oct 2014
TL;DR: In this article, the general expression of the sth (s in N if n is odd; s in Z if N is even) power of some tridiagonal matrices was derived.
Abstract: In this paper, we derive the general expression of the sth (s in N if n is odd; s in Z if n is even) power of some tridiagonal matrices.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |