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: A new kind of prism element with a triangular base is presented for discretization of multi-scale layered structures within the discontinuous Galerkin time-domain framework that combines the flexibility of triangles with the accuracy of spectral elements for layered structures.
Abstract: A new kind of prism element with a triangular base is presented for discretization of multi-scale layered structures within the discontinuous Galerkin time-domain framework. Mixed-order curl-conforming vector basis functions are used in the triangular bases of the prismatic element. The height of the prism adopts spectral basis functions based on Gauss–Lobatto–Legendre polynomials, with an arbitrary order of interpolation. This method combines the flexibility of triangles with the accuracy of spectral elements for layered structures. Eigenvalues obtained show better results than traditional finite elements using tetrahedrons and hexahedrons. For transient analysis, the implicit Crank–Nicholson method is implemented for sequential sub-domains. This kind of arrangement of sub-domains produces a block tridiagonal linear system, thus allowing a block Thomas algorithm to solve the system efficiently. A package-to-chip example shows the efficacy of this method.
6 citations
TL;DR: This paper has developed portable cyclic reduction and SPIKE algorithm OpenCL implementations with the intent to target a range of co-processors in a heterogeneous computing environment including Field Programmable Gate Arrays (FPGAs), Graphics Processing Units (GPUs) and other multi-core processors.
Abstract: Tridiagonal diagonally dominant linear systems arise in many scientific and engineering applications. The standard Thomas algorithm for solving such systems is inherently serial forming a bottleneck in computation. Algorithms such as cyclic reduction and SPIKE reduce a single large tridiagonal system into multiple small independent systems which can be solved in parallel. We have developed portable cyclic reduction and SPIKE algorithm OpenCL implementations with the intent to target a range of co-processors in a heterogeneous computing environment including Field Programmable Gate Arrays (FPGAs), Graphics Processing Units (GPUs) and other multi-core processors. In this paper, we evaluate these designs in the context of solver performance, resource efficiency and numerical accuracy.
6 citations
18 Jun 2006
TL;DR: This work proposes multisection for the multiple eigenvalues (MME) method for determining the eigen values of symmetric tridiagonal matrices, and shows how to optimize its performance by dynamically selecting the implementation parameters.
Abstract: We propose multisection for the multiple eigenvalues (MME) method for determining the eigenvalues of symmetric tridiagonal matrices. We also propose a method using runtime optimization, and show how to optimize its performance by dynamically selecting the implementation parameters. Performance results using a Hitachi SR8000 supercomputer with eight processors per node yield (1) up to 6.3x speedup over a conventional multisection method, and (2) up to 1.47x speedup over a statically optimized MME method.
6 citations
TL;DR: Refined perturbation bounds are developed that generalize Skeel bounds to the case of ill conditioned systems and reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems are developed.
Abstract: We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.
6 citations
TL;DR: In this paper, an algorithm for obtaining the inverse of a tridiagonal matrix numerically is presented. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient.
Abstract: This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient.
6 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |