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: The explicit structure of the inverse of block tridiagonal matrices is presented in terms of blocks defined by linear recurrence relations, and parallel algorithms are shown which solve block second order linear recurrences without using commutativity.
TL;DR: This paper presents several implementations for the parallel solving of large tridiagonal systems on multi-core architectures, using the OmpSs programming model, based on the combination of two different existing algorithms, PCR and Thomas.
Abstract: Many problems of industrial and scientific interest require the solving of tridiagonal linear systems. This paper presents several implementations for the parallel solving of large tridiagonal systems on multi-core architectures, using the OmpSs programming model. The strategy used for the parallelization is based on the combination of two different existing algorithms, PCR and Thomas. The Thomas algorithm, which cannot be parallelized, requires the fewest number of floating point operations. The PCR algorithm is the most popular parallel method, but it is more computationally expensive than Thomas. The method proposed in this paper starts applying the PCR algorithm to break down one large tridiagonal system into a set of smaller and independent ones. In a second step, these independent systems are concurrently solved using Thomas. The paper also contains an analytical study of which is the best point to switch from PCR to Thomas. Also, the paper addresses the main performance issues of combining PCR and Thomas proposing a set of alternative implementations, some of them even imply algorithmic changes. The performance evaluation shows that the best implementation achieves a peak speedup of 4 with respect to the Intel MKL counterpart routine and 2.5 with respect to a single-threaded Thomas.
TL;DR: In this article, the standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction.
TL;DR: In this paper, an analytical formula for the inversion of symmetrical tridiagonal matrices is presented, which is of relevance to the solution of a variety of problems in mathematics and physics.
Abstract: In this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices. The result is of relevance to the solution of a variety of problems in mathematics and physics. As an example, the formula is used to derive an exact analytical solution for the one-dimensional discrete Poisson equation with Dirichlet boundary conditions.
TL;DR: In this paper, the class of tridiagonal 2-to-plitz matrices is studied, and explicit and implicit formulas for eigenpairs of these matrices are given.
Abstract: with cd ^ 0, other entries a^ being zero. Shin gives explicit formulas for eigenpairs ofmatrix (1) when the order n is odd, and implicit formulas, for n even.The purpose of this note is to draw attention to a paper [3], with which Shin wasobviously unfamiliar. In [3], the class of so-called tridiagonal 2-Toeplitz matrices isstudied. These are tridiagonal matrices that satisfy the relation(2) a
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |