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: Lower bounds are presented that hold when the number of data items per processor is bounded, are general lower bounds, and for specific data layouts commonly used in designing parallel algorithms to solve tridiagonal linear systems.
Abstract: The problem of solving tridiagonal linear systems on parallel distributed-memory environments is considered in this paper. In particular, two common direct methods for solving such systems are considered: odd-even cyclic reduction and prefix summing. For each method, a variety of lower bounds on execution time for solving tridiagonal linear systems are presented. Specifically, lower bounds are presented that (a) hold when the number of data items per processor is bounded, (b) are general lower bounds, and (c) for specific data layouts commonly used in designing parallel algorithms to solve tridiagonal linear systems. Furthermore, algorithms are presented that have running times within a constant factor of the lower bounds provided. Lastly, a comparison of bounds for odd-even cyclic reduction and prefix summing is given.
6 citations
IBM1
TL;DR: Time measurements show impressive speed-ups over the domino ( ) function and the APL2 versions of the Gaussian elimination method, specialized for cyclic tridiagonal andtridiagonal systems.
Abstract: An APL2 function is presented for solving cyclic tridiagonal and tridiagonal systems of linear equations Those systems frequently occur in various areas, e g interpolation by spline functions, numerical solution of elliptic differential equations, etc The function is based on a modification of the cyclic reduction method [1], [2] Time measurements show impressive speed-ups over the domino ( ) function and the APL2 versions of the Gaussian elimination method, specialized for cyclic tridiagonal and tridiagonal systems
6 citations
TL;DR: To improve on the shortcomings observed in symbolic algorithms introduced recently for related matrices, a reliable numerical solver is proposed for computing the solution of the matrix linear equation A X = B .
6 citations
Posted Content•
TL;DR: In this paper, the correspondence between finite sequences of finitely ported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices has been analyzed and an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean structure on matrices is given.
Abstract: We analyze the correspondence between finite sequences of finitely sup- ported probability distributions and finite-dimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean structure on matrices. Our results provide an analytical tool with which to study ensembles of tridiagonal matrices, important in certain inverse problems and integrable systems. As an application, we prove that the Euler characteristic of any generic isospectral set of symmetric, tridiagonal matrices is a tangent number.
6 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |