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
Proceedings Article•
21 Oct 2013TL;DR: In this paper, an energy conservation principle motivated approach is proposed to construct physically correct tridiagonal dissipative structures, and some conceptually new results are presented, too, leading to a new class of physically correct dissipative structure.
Abstract: Computation complexity of a broad variety of practical design problems is known to be strongly depending on an algebraic complexity of corresponding mathematical system representations. Especially some large scale electro dynamical and/or thermodynamic structures often lead to mathematical models of infinite or nearly infinite dimensionality. One way to overcome the complexity problems is based on some special algebraic structures of low order model approximations, such as e.g. balanced representations. An alternative approach is based on the concept of tridiagonal system representations [1]. In this contribution an energy conservation principle motivated approach [2], [3], [4], leading to a new class of physically correct tridiagonal dissipative structures [4] is proposed, and some conceptually new results are presented, too.
3 citations
31 Dec 1993
TL;DR: A new parallel algorithm for solving periodic tridiagonal Toeplitz linear systems of equations is presented, based on a modified Gaussian elimination, and it requires a continued fraction and its analytic solution during the decompose phase to minimize the decomposition overhead.
Abstract: A new parallel algorithm for solving periodic tridiagonal Toeplitz linear systems of equations is presented. This algorithm is designed for computers with a limited number of processors. It is a combination of the Kim and Lee algorithm, and a bordering method. Kim and Lee algorithm is based on a modified Gaussian elimination, and it requires a continued fraction and its analytic solution during the decomposition phase to minimize the decomposition overhead. The proposed algorithm is implemented on an Intel iPSC/2 hypercube and attained an almost linear speedup.
3 citations
TL;DR: It is proved that for a given real symmetric tridiagonal interval matrices, it can achieve its exact range of the smallest and largest eigen values just by computing extremal eigenvalues of four symmetrictridiagonal matrices.
Abstract: Summary
Computing the extremal eigenvalue bounds of interval matrices is non-deterministic polynomial-time (NP)-hard. We investigate bounds on real eigenvalues of real symmetric tridiagonal interval matrices and prove that for a given real symmetric tridiagonal interval matrices, we can achieve its exact range of the smallest and largest eigenvalues just by computing extremal eigenvalues of four symmetric tridiagonal matrices.
3 citations
Posted Content•
TL;DR: The author presents reliable symbolic algorithms for solving a general bordered tridiagonal linear system based on The Sherman-Morrison-Woodbury formula and the computational cost of it is O(n).
Abstract: In this paper, the author present reliable symbolic algorithms for solving a general bordered tridiagonal linear system. The first algorithm is based on the LU decomposition of the coefficient matrix and the computational cost of it is O(n). The second is based on The Sherman-Morrison-Woodbury formula. The algorithms are implementable to the Computer Algebra System (CAS) such as MAPLE, MATLAB and MATHEMATICA. Three examples are presented for the sake of illustration.
3 citations
1 May 1993
TL;DR: A thorough performance exposure and exploitation of a MIMD computer complex is carried out by presenting a selection of algorithms which implement a certain parallel evaluation routing and search for the optimal values of the granularity factor in accordance with some sequential subroutines permitted in the solution phase.
Abstract: A thorough performance exposure and exploitation of a MIMD computer complex is carried out by presenting a selection of algorithms which implement a certain parallel evaluation routing and search for the optimal values of the granularity factor in accordance with some sequential subroutines permitted in the solution phase for most of the available parallel constructs of the machine in hand. For the cyclic odd-even reduction technique the symmetric constant-diagonal periodic case is chosen as the experimental vehicle, since it is more complicated and its concept indirectly includes that of the corresponding non-periodic case.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |