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
TL;DR: The story of Gauss, the algorithm of choice for the solution of dense linear systems of equations, and its relation to his probabilistic development of least squares is told.
Abstract: Gaussian elimination is the algorithm of choice for the solution of dense linear systems of equations. However, Gauss himself originally introduced his elimination procedure as a way of determining the precision of least squares estimates and only later described the computational algorithm. This article tells the story of Gauss, his algorithm, and its relation to his probabilistic development of least squares.
36 citations
TL;DR: In this paper, an analytical form for the inversion of general periodic tridiagonal matrices is presented, which leads to closed formulae for some special cases such as symmetric or perturbed Toeplitz for both periodic and non-periodic matrices.
36 citations
TL;DR: An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method is proposed in this paper and the experimental results show that the parallel algorithm is in good agreement with the analytic solution.
Abstract: An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method is proposed in this paper. The parallel algorithm consists of a parallel solver for linear tridiagonal equations and parallel vector arithmetic operations. For the parallel solver, in order to solve the linear tridiagonal equations efficiently, a new tridiagonal reduced system is developed with an elimination method. The experimental results show that the parallel algorithm is in good agreement with the analytic solution. The parallel implementation with 16 parallel processes on two eight-core Intel Xeon E5-2670 CPUs is 14.55 times faster than the serial one on single Xeon E5-2670 core.
36 citations
TL;DR: This algorithm combines the advantages of existing algorithms such as QR, bisection/multisection, and Cuppen’s divide-and-conquer method and is fully parallel and competitive in speed with the most efficient QR algorithm in serial mode.
Abstract: This paper presents an algorithm for the eigenvalue problem of symmetric tridiagonal matrices. The algorithm employs the determinant evaluation, split-and-merge strategy, and the Laguerre iteration. The method directly evaluates eigenvalues and uses inverse iteration as an option when eigenvectors are needed. This algorithm combines the advantages of existing algorithms such as QR, bisection/multisection, and Cuppen’s divide-and-conquer method. It is fully parallel and competitive in speed with the most efficient QR algorithm in serial mode. On the other hand, the algorithm is as accurate as any standard algorithm for the symmetric tridiagonal eigenproblem and enjoys the flexibility in evaluating partial spectrum.
36 citations
TL;DR: Either bounds for the inverse or numerical methods for solving linear systems may be derived in the factorization of five-diagonal matrices as the product of two Toeplitz tridiagonalMatrices.
36 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |