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, two new proofs are given of the following characterization theorem of M. Fiedler: if Cn, n⩾2, be the class of all symmetric, real matrices A of order n with the property that rank (A + D) ⩾ n - 1 for any diagonal real matrix D, then there exists a permutation matrix P such that PAPT is tridiagonal and irreducible.
13 citations
Journal Article•
TL;DR: In this article, a class of asymptotically stable nonlinear systems with a special tridiagonal structure is proposed for the purpose of designing controllers, where the origin system can be transformed into a system with special tridagonal structure by controllers or some coordinates transformations, these controllers are the stabilizing controllers.
13 citations
TL;DR: In this paper, a mathematical model is chosen and a finite-difference algorithm is developed to describe the drying of agro products in a batch fluidized bed, and the model is discretized according to the implicit scheme for two particle geometries: sphere and chip.
Abstract: A mathematical model is chosen and a finite-difference algorithm is developed to describe the drying of agro products in a batch fluidized bed. The mathematical model is discretized according to the implicit scheme for two particle geometries: sphere and chip. The system of algebraic equations is solved using the tridiagonal matrix algorithm (TDMA). Stability and convergence of the numerical algorithm are analyzed by variation of the time step and mesh size, finding computer time savings when using nonuniform space steps and boundary conditions are discretized using three nodal positions. Obtained results are compared with numerical results from the literature and experimental data of potato chips drying, concluding that the chosen model describes the phenomena correctly.
13 citations
TL;DR: A semi-implicit time discretization scheme is applied, enabling stable computation of mask synthesis with large time steps and merit the superiority of the proposed semi- Implicit approach with improved convergence performance.
Abstract: Inverse lithography techniques (ILT) have been extensively used by the semiconductor industry to compensate for the inherent image distortions in optical lithography. However, the iterative ILT optimization procedure requires rather prohibitive time steps leading to poor efficiency with explicit time discretization. In this paper, a semi-implicit time discretization scheme is applied, enabling stable computation of mask synthesis with large time steps. Additive operator splittering (AOS) is implemented with respect to coordinate axes, reducing mask synthesis to consecutive one-dimensional updates represented by tridiagonal linear equations, which is solved efficiently by the Thomas algorithm. Simulation results merit the superiority of the proposed semi-implicit approach with improved convergence performance.
13 citations
1 Jan 2011
TL;DR: In this article, the one dimensional mixed-form of Richards Equation (RE) was solved by simple control volume method and the principle of this method is the integrating RE in a domain.
Abstract: In this research, the one dimensional mixed-form of Richards Equation (RE) was solved by simple control volume method. The principle of this method is the integrating RE in a domain. This method avoids mass-balance errors and is numerically stable. The resulting tri diagonal matrix was solved by using of Thomas algorithm in each iteration level. The performance of method is assessed on test cases and show capability of mass conservative finite volume.
13 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |