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
IBM1
TL;DR: A new (partition) method for solving a tndiagonal system of lmear equations is presented and various situations under which the partmon method can be preferable are described.
Abstract: A new (partition) method for solving a tndiagonal system of lmear equations is presented in this paper The method is suitable for both parallel and vector computers. Although the partition method has a shghtly higher vector operatmn count than those of the two competing methods (the recursive doubling method and the cychc reduction method), it has a scalar count much smaller than that of the recursive doubling. The scalar counts between the partition method and the cyclic reduction method are so close as to make a timing evaluation inconclusive without considering the data management problem, especmlly when large systems are solved. Various situations under which the partmon method can be preferable are described.
278 citations
TL;DR: A new, stable method for finding the spectral decomposition of a symmetric arrowhead matrix and a new implementation of deflation are presented, which are competitive with bisection with inverse iteration, Cuppen's divide-and-conquer algorithm, and the QR algorithm for solving the symmetric tridiagonal eigenproblem.
Abstract: The authors present a stable and efficient divide-and-conquer algorithm for computing the spectral decomposition of an $N \times N$ symmetric tridiagonal matrix. The key elements are a new, stable method for finding the spectral decomposition of a symmetric arrowhead matrix and a new implementation of deflation. Numerical results show that this algorithm is competitive with bisection with inverse iteration, Cuppen's divide-and-conquer algorithm, and the QR algorithm for solving the symmetric tridiagonal eigenproblem.
264 citations
1 Jan 2008
246 citations
Book•
1 Jan 2001TL;DR: In this article, the authors present a general generalized Eigensystem for simple tridiagonal matrices and a semi-discrete approach to choose a time-Marching method.
Abstract: 1. Introduction.- 2. Conservation Laws and the Model Equations.- 3. Finite-Difference Approximations.- 4. The Semi-Discrete Approach.- 5. Finite-Volume Methods.- 6. Time-Marching Methods for ODE'S.- 7. Stability of Linear Systems.- 8. Choosing a Time-Marching Method.- 9. Relaxation Methods.- 10. Multigrid.- 11. Numerical Dissipation.- 12. Split and Factored Forms.- 13. Analysis of Split and Factored Forms.- Appendices.- A. Useful Relations from Linear Algebra.- A.1 Notation.- A.2 Definitions.- A.3 Algebra.- A.4 Eigensystems.- A.5 Vector and Matrix Norms.- B. Some Properties of Tridiagonal Matrices.- B.1 Standard Eigensystem for Simple Tridiagonal Matrices.- B.2 Generalized Eigensystem for Simple Tridiagonal Matrices.- B.3 The Inverse of a Simple Tridiagonal Matrix.- B.4 Eigensystems of Circulant Matrices.- B.4.1 Standard Tridiagonal Matrices.- B.4.2 General Circulant Systems.- B.5 Special Cases Found from Symmetries.- B.6 Special Cases Involving Boundary Conditions.- C. The Homogeneous Property of the Euler Equations.
240 citations
TL;DR: The numerical approximate solutions to the Burgers’ equation have been computed without transforming the equation and without using the linearization.
223 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |