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 paper, the authors proposed an algorithm based on the splitting method combined with the tridiagonal matrix algorithm to solve auxiliary systems of two-point equations to accelerate the convergence of inner iterations.
Abstract: A $$K{{P}_{1}}$$
scheme for accelerating the convergence of inner iterations is constructed for the transport equation in 2D $$r,z$$
geometry. This scheme is consistent with the nodal LD (Linear Discontinues) and LB (Linear Best) schemes of the third and fourth orders of accuracy with respect to the spatial variables. To solve the $${{P}_{1}}$$
system for acceleration corrections, an algorithm is proposed based on the splitting method combined with the tridiagonal matrix algorithm to solve auxiliary systems of two-point equations. A modification of the algorithm for 2D $$x,z$$
geometry is considered. Numerical examples of using the $$K{{P}_{1}}$$
scheme to solve radiation transport problems in 2D $$r,z$$
, $$x,z$$
, and $$r,\vartheta $$
geometries are given, including problems with a significant role of scattering anisotropy and highly heterogeneous problems with dominant scattering.
1 citations
23 Jan 2015
TL;DR: In this paper, the authors discuss the solution of singularly perturbed differential-difference equations exhibiting dual layer using the higher order finite differences, and analyze the effect of the parameters on the solution.
Abstract: In this paper, we discuss the solution of singularly perturbed differential-difference equations exhibiting dual layer using the higher order finite differences. First, the second order singularly perturbed differential-difference equations is replaced by an asymptotically equivalent second order singular perturbed ordinary differential equation. Then, fourth order stable finite difference scheme is applied to get a three term recurrence relation which is easily solved by Thomas algorithm. Some numerical examples have been solved to validate the computational efficiency of the proposed numerical scheme. To analyze the effect of the parameters on the solution, the numerical solution has also been plotted using graphs. The error bound and convergence of the method have also been established.
1 citations
21 Jun 2000
TL;DR: An efficient parallel algorithm, which is dubbed farmzeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with 112 nodes and produces more accurate eigenvalues than the QR method.
Abstract: An efficient parallel algorithm, which we dubbed farmzeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with 112 nodes [1]. The basis of our parallel implementation is an improved version of the zeroinNR method [2]. It is consistently faster than simple bisection and produces more accurate eigenvalues than the QR method. As it happens with bisection, zeroinNR exhibits great flexibility and allows the computation of a subset of the spectrum with some prescribed accuracy. Results were carried out with matrices of different types and sizes up to 104 and show that our algorithm is efficient and scalable.
1 citations
28 Jul 2020
TL;DR: In this article, the authors presented an exponentially fitted spline method to solve SPDDE with dual layer, where the given second order differential-difference equation is replaced by an asymptotically proportionate second order singular perturbation problem.
Abstract: In this paper, we presented exponentially fitted spline method to solve SPDDE with dual layer. At first, the given second order differential-difference equation is replaced by an asymptotically proportionate second order singular perturbation problem. At that point, a fitting factor is brought into the exponentially fitted spline Method. The value of fitting factor is obtained by the singular perturbations theory. The Thomas algorithm is used to solve the tridiagonal system obtained by the method. The result of the delay and also advance parameters on the boundary layer(s) has likewise been evaluated as well as represented in charts. The applicability of the proposed plan is actually confirmed through executing it on model examples. To show the accuracy of the method, the results are presented in terms of maximum absolute errors for arbitrary λ1, λ2 such that λ1 +λ2 =1/2.
1 citations
TL;DR: In this paper, a fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval.
Abstract: A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of singular perturbations. Thomas Algorithm (also known as Discrete Invariant Imbedding Algorithm) is used to solve the resulting tri-diagonal system. To validate the applicability of the method, some linear and non-linear examples have been solved for different values of the perturbation parameter. The numerical results are tabulated and compared with exact solutions. The error bound and convergence of the proposed method has also been established. From the results, it is observed that the present method approximates the exact solution very well. Key words : Singular perturbation problems, stable, central differences, fitted methods
1 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |