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
Posted Content•
TL;DR: In this paper, a method for computing solutions of infinite dimensional nonlinear operators with a tridiagonal dominant linear part was proposed, where the authors recast the operator equation into an equivalent Newton-like equation.
Abstract: We present a method designed for computing solutions of infinite dimensional non linear operators $f(x) = 0$ with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation $x = T(x) = x - Af(x)$, where $A$ is an approximate inverse of the derivative $Df(\overline x)$ at an approximate solution $\overline x$. We present rigorous computer-assisted calculations showing that $T$ is a contraction near $\overline x$, thus yielding the existence of a solution. Since $Df(\overline x)$ does not have an asymptotically diagonal dominant structure, the computation of $A$ is not straightforward. This paper provides ideas for computing $A$, and proposes a new rigorous method for proving existence of solutions of nonlinear operators with tridiagonal dominant linear part.
TL;DR: In this article , a hybrid multigrid-Thomas algorithm was proposed to solve Poisson's equation as part of the spatial discretization of a time-evolving PDE system.
15 Aug 2004
TL;DR: The improved version of P-scheme works well for smaller problems on distributed environment like PC cluster systems and linear and super-linear speedups can be achieved for 8194 x 8194 and 16386 x 16386 problems, respectively.
Abstract: We propose ?P-scheme? for solving recurrence equations for a tridiagonal linear system of equations on distributed-memory parallel computers, but its effectiveness is limited to the case where the problem is enough large. The limitation is mainly due to the communication cost of propagation phase of P-scheme. In order to overcome the difficulty, we use ?message vectorization?, which aggregates several communication messages into one, to alleviates the communication cost of P-scheme and evaluate the effectiveness of message vectorization for tridiagonal matrix solver. Our experiments prove that the improved version of P-scheme works well for smaller problems on distributed environment like PC cluster systems and show linear and super-linear speedups can be achieved for 8194 x 8194 and 16386 x 16386 problems, respectively.
TL;DR: The estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices are given.
Abstract: The theory and method of matrix computation, as an important tool, have much important applications such as in computational mathematics, physics, image processing and recognition, missile system design, rotor bearing system, nonlinear kinetics, economics and biology etc. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices.
Posted Content•
TL;DR: In this article, the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE BVPs, is reviewed.
Abstract: In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution of ODEs.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |