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
22 May 2005
TL;DR: The method discussed transforms the matrix into structured triangular form and has several attractive properties: the block tridiagonal structure is fully exploited; high data locality is achieved, which is important for high efficiency on modern computer systems.
Abstract: A method for computing orthogonal URV/ULV decompositions of block tridiagonal (or banded) matrices is presented. The method discussed transforms the matrix into structured triangular form and has several attractive properties: The block tridiagonal structure is fully exploited; high data locality is achieved, which is important for high efficiency on modern computer systems; very little fill-in occurs, which leads to no or very low memory overhead; and in most practical situations observed the transformed matrix has very favorable numerical properties. Two variants of this method are introduced and compared.
1 citations
TL;DR: It is shown classical elimination procedure can be simply extended to uncouple partitioned tridiagonal systems for parallel processing of their solution by way of Wang's method.
Abstract: We show classical elimination procedure can be simply extended to uncouple partitioned tridiagonal systems for parallel processing of their solution. In each block of equations, we now need two simultaneous eliminations; one usual forward elimination and one backward from across the succeeding block. Significantly, unlike Wang's method [6], our is a one-stage elimination procedure, at the end of which the core system is reached. Once the core system is solved, the uncoupled subsystems are solved in parallel by back substitution.
1 citations
TL;DR: This paper proposes a new mapping of the Cyclic Elimination (CE) algorithm for the solution of block tridiagonal linear system of equations onto hypercube multiprocessors using both analytical and simulation methods.
Abstract: In this paper, we propose a new mapping of the Cyclic Elimination (CE) algorithm for the solution of block tridiagonal linear system of equations onto hypercube multiprocessors Unlike the previous mapping schemes, in our mapping of the CE algorithm all communications are restricted to physically adjacent processors, using the concept of data replication The effectiveness of our mapping is demonstrated by comparing it with the existing mapping of the Cyclic Reduction algorithm onto hypercubes using both analytical and simulation methods
1 citations
1 Jan 2017
TL;DR: Unbounded solutions (critical blow-up regimes) simulated by the 3D nonlinear diffusion equation in a spherical shell are studied and the coordinate splitting of the differential operator coupled with two spherical coordinate maps makes it possible to use periodic boundary conditions in the latitudinal and longitudinal directions.
Abstract: Unbounded solutions (critical blow-up regimes) simulated by the 3D nonlinear diffusion equation in a spherical shell are studied. The coordinate splitting of the differential operator coupled with two spherical coordinate maps makes it possible to use periodic boundary conditions in the latitudinal and longitudinal directions and employ the computationally efficient Sherman-Morrison formula and Thomas algorithm. The resulting finite difference method is direct, with implicit and unconditionally stable schemes of second-order approximation in all the variables. Numerical tests demonstrate that it allows simulating different blow-up regimes in complex computational domains.
1 citations
11 Jun 1991
TL;DR: A new parallel algorithm is presented for computing the determinant of a tridiagonal matrix based on a divide-and-conquer strategy and has a parallel time complexity of O(log/sub 2/n).
Abstract: A new parallel algorithm is presented for computing the determinant of a tridiagonal matrix The algorithm is based on a divide-and-conquer strategy and has a parallel time complexity of O(log/sub 2/n) The algorithm is adaptive and the effect of the available number of processors on the computation time is studied on a simulated MIMD static dataflow machine >
1 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |