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
1 Jan 1993
TL;DR: This work presents an algorithm that efficiently computes only the elements of the inverse at locations corresponding to nonzero elements in the original matrix in O(n) time and memory, useful in solving discretized systems of partial differential equations that arise when computing electrical flow along a branched structure.
Abstract: Standard algorithms for computing the inverse of a tridiagonal matrix (or more generally, any Hines matrix) compute the entire inverse, which is not sparse. For some problems, only the elements of the inverse at locations corresponding to nonzero elements in the original matrix are required. We present an algorithm that efficiently computes only these elements in O(n) time and memory. This algorithm is useful in solving discretized systems of partial differential equations that arise when computing electrical flow along a branched structure, such as a neuron’s dendritic arbor.
4 citations
4 citations
TL;DR: An efficient numerical algorithm for evaluating the determinants of general bordered k-tridiagonal matrices in linear time based on a novel incomplete block-diagonalization approach which preserves the low-rank structure and sparsity of the original matrix and its competitiveness with Gaussian elimination algorithm and MATLAB built-in function.
4 citations
Journal Article•
TL;DR: In this article, the general expression of the r th power (r ∈ N) for one type of tridiagonal matrix was derived, where n is the number of vertices in the tridiagon.
Abstract: In this paper, we derive the general expression of the r th power (r ∈ N) for one type of tridiagonal matrix.
4 citations
TL;DR: A cost criterion function for choosing the optimal pivot at each stage of the Gaussian elimination method is described, which takes into consideration both the fill-in and the number of arithmetical operations.
Abstract: In this note, a cost criterion function for choosing the optimal pivot at each stage of the Gaussian elimination method is described It takes into consideration both the fill-in and the number of arithmetical operations Other known criterion functions byTewarson [4] andMarkowitz [6] are also discussed and compared with the new criterion function
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |