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, a 1D active magnetic regenerator model developed at the University of Applied Sciences of Western Switzerland is described, which is implemented in MATLAB and it has a graphical user interface.
Abstract: The 1D active magnetic regenerator model developed at the University of Applied Sciences of Western Switzerland is described. The system of two partial differential equations is discretized with the finite differences method backward in time and solved with the tridiagonal matrix algorithm. New features, not found in the literature in 1D models, are thermal losses in the regenerator, parasitic heat exchange, and the calculation of the AMR cycle output power in steady state. The model is implemented in MATLAB and it has a graphical user interface.
21 citations
TL;DR: An iterative algorithm for finding Hermitian tridiagonal solution with the least norm to the quaternionic least squares problem by making the best use of structure of real representation matrices is given.
21 citations
TL;DR: Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance, yielding a representation of the error matrix for the factorization and for the solution of the linear system.
Abstract: Tridiagonal systems play a fundamental role in matrix computation. In particular, in recent years parallel algorithms for the solution of tridiagonal systems have been developed. Among these, the cyclic reduction algorithm is particularly interesting. Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance. A backward error analysis is made, yielding a representation of the error matrix for the factorization and for the solution of the linear system. The results are compared with those for LU factorization.
21 citations
TL;DR: In this paper, it was shown that if forcing is applied at an interior point, then the reconstruction is unique if that point is not a node of any eigenmode; if it is, there is a family of systems with the required properties.
Abstract: It is known that a simple spring-mass system may be reconstructed uniquely (apart from a single scaling factor) from the poles and zeros of the frequency response function corresponding to sinusoidal forcing at an end. The (squares of the) poles yield the eigenvalues of a tridiagonal matrix, A, while the zeros yield the eigenvalues of the matrix, A*, with the last row and column deleted. There are proven numerical methods for reconstructing A. The authors show that, if forcing is applied at an interior point, then the reconstruction is unique if that point is not a node of any eigenmode; if it is, there is a family of systems with the required properties. In either case the system may be constructed using modifications of proven techniques.
20 citations
TL;DR: This paper is mainly devoted to constructing symbolic algorithms for solving tridiagonal linear systems of equations via transformations via transformations, and the computational cost of these algorithms is given.
Abstract: Numeric algorithms for
solving the linear systems of tridiagonal type have already existed. The
well-known Thomas
algorithm is an example of such algorithms. The current paper is mainly devoted
to constructing symbolic
algorithms for solving tridiagonal linear systems of equations via
transformations. The new symbolic algorithms remove the cases where the numeric
algorithms fail. The computational cost of these algorithms is given. MAPLE procedures based on these
algorithms are presented. Some illustrative examples are given.
20 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |