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
4 Nov 2010
TL;DR: Inverse M-matrices have wide applications as discussed by the authors, and they have been used in many applications, e.g., for diagraph theory and the properties of inverse matrix completion.
Abstract: Inverse M-matrices have wide applications. In the paper, we discuss the completion problems and algorithms for two special partial inverse M-matrices: the tridiagonal partial inverse M-matrix and the partial matrix whose graph is acyclic without specified paths. By using the diagraph theory and the properties of inverse M-matrices, we give its completion theorems and the corresponding completion algorithms.
1 Dec 1977
TL;DR: In this paper, a nonsingular transformation matrix T that relates the state triple (AT, BT, CT) of tridiagonal to state triple of phase canonical linear system is given.
Abstract: A nonsingular transformation matrix T that relates the state triple (AT, BT, CT) of tridiagonal to state triple (Ap,Bp,Cp) of phase canonical linear system is given. The simple rules for evaluating the entries of matrix T arc also included.
1 Aug 2015
TL;DR: This paper evaluated the parallel algorithms for solving penta-diagonal linear systems-Gaussion elimination by their execution time and found the cyclic reduction algorithm is more efficient than the Gaussion algorithm.
Abstract: According to the parallel algorithms for solving tridiagonal linear systems, we studied the parallel algorithms for solving penta-diagonal linear systems. In the parallel solutions for tridiagonal linear systems—cyclic reduction method (CR), recursive doubling method (RD) and the partition method (PD), however, only the cyclic reduction algorithm can be used to solve the penta-diagonal linear systems. Compared with the serial algorithm of solving penta-diagonal linear systems—Gaussion elimination, cyclic reduction algorithm has obvious advantages. In this paper, we evaluated these methods by their execution time. According to the measured datas, the cyclic reduction algorithm has been implemented via multi-threads. The efficiency of Cyclic reduction algorithm is more efficient than the Gaussion algorithm by 23.74%.
Journal Article•
TL;DR: For a given set of real or complex numbers with nonnegative summation, this paper introduced some special conditions that with them there is no nonnegative tridiagonal matrix in which is its spectrum.
Abstract: In this paper, at rst for a given set of real or complex numbers with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices. c
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |