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
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Papers
TL;DR: A novel linear equation solution method based on a row elimination back-substitution method that is much faster and requires less storage than the Gaussian elimination algorithm and, therefore, is capable of solving larger systems of equations.
Abstract: In this paper, a novel linear equation solution method is proposed based on a row elimination back-substitution method (REBSM) The elimination and back-substitution procedures are carried out on individual row levels The advantage of the proposed method is that it is much faster and requires less storage than the Gaussian elimination algorithm and, therefore, is capable of solving larger systems of equations The method is particularly efficient for solving band diagonal sparse systems with symmetric or nonsymmetric coefficient matrices, and can be easily applied to popular numerical methods, such as the finite element method and the boundary element method Detailed Fortran codes and examples are given to demonstrate the robustness and efficiency of the proposed method
5 citations
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TL;DR: This paper analyzes the Rauch-Tung-Striebel (RTS) and Mayne-Fraser (MF) smoothers from an optimization and algebraic perspective, revealing new insights on their numerical stability properties.
Abstract: The Rauch-Tung-Striebel (RTS) and the Mayne-Fraser (MF) algorithms are two of the most popular smoothing schemes to reconstruct the state of a dynamic linear system from measurements collected on a fixed interval. Another (less popular) approach is the Mayne (M) algorithm introduced in his original paper under the name of Algorithm A. In this paper, we analyze these three smoothers from an optimization and algebraic perspective, revealing new insights on their numerical stability properties. In doing this, we re-interpret classic recursions as matrix decomposition methods for block tridiagonal matrices.
First, we show that the classic RTS smoother is an implementation of the forward block tridiagonal (FBT) algorithm (also known as Thomas algorithm) for particular block tridiagonal systems. We study the numerical stability properties of this scheme, connecting the condition number of the full system to properties of the individual blocks encountered during standard recursion. Second, we study the M smoother, and prove it is equivalent to a backward block tridiagonal (BBT) algorithm with a stronger stability guarantee than RTS. Third, we illustrate how the MF smoother solves a block tridiagonal system, and prove that it has the same numerical stability properties of RTS (but not those of M). Finally, we present a new hybrid RTS/M (FBT/BBT) smoothing scheme, which is faster than MF, and has the same numerical stability guarantees of RTS and MF.
5 citations
TL;DR: This work presents a new algorithm for inverting tridiagonal matrices inspired by the recursive partitioning algorithm of Evans and has potential for its vector and parallel implementation.
Abstract: Motivated by the recursive partitioning algorithm of Evans [2], we present a new algorithm for inverting tridiagonal matrices. Our derivation of the algorithm is different but elementary. The present algorithm has potential for its vector and parallel implementation.
5 citations
TL;DR: In this paper, an iterative scheme for the calculation of eigenvalues of tridiagonal matrices is defined in terms of successive partitionings, and a method for computing all eigen values of such a matrix is defined.
5 citations
4 Aug 2020
TL;DR: In this paper, the authors presented a time scale dimensionless model that considers charge carrier motion and ion migration in a perovskite solar cell, which provides high accuracy accompanied by the use of realistic parameters.
Abstract: An important tool for explaining the hysteretic behavior in movement of electronic and ionic charges is drift-diffusion model. Adding numerical methods to these models in realistic operation situations is challenging due to the fact that some parameters have extreme values. We present a time scale dimensionless model that considers charge carrier motion and ion migration in a perovskite solar cell. The proposed model provides high accuracy accompanied by the use of realistic parameters. In order to solve matrix and equations, tridiagonal matrix algorithm (TDMA) method is exploited. Electric potential, density of ion vacancy migration, hole and electron concentration characteristics are calculated and illustrated in transient time scale. Besides, the mentioned characteristics are illustrated with different feasible built-in potential. This approach gives insight into device physics, charge transport model, ion migration and hysteresis phenomena.
5 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |