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: A graph-theoretic algorithm which examines an arbitrary n × n matrix and determines whether or not it can be permuted into tridiagonal form is given and gives the explicit tridiagon form.
Abstract: Tridiagonalizing a matrix by similarity transformations is an important computational tool in numerical linear algebra. Consider the class of sparse matrices which can be tridiagonalized using only row and corresponding column permutations. The advantages of using such a transformation include the absence of round-off errors and improved computation time when compared with standard transformations. A graph-theoretic algorithm which examines an arbitrary n × n matrix and determines whether or not it can be permuted into tridiagonal form is given. The algorithm requires no arithmetic while the number of comparisons, the number of assignments, and the number of increments are linear in n. This compares very favorably with standard transformation methods. If the matrix is permutable into tridiagonal form, the algorithm gives the explicit tridiagonal form. Otherwise, early rejection will occur.
10 citations
TL;DR: A modified form of the AGE iterative algorithm for solving a tridiagonal system of linear equations is presented and is shown to require reduced computational effort and have similar convergence and stability properties to the previous AGE scheme.
Abstract: In this short paper, a modified form of the AGE iterative algorithm for solving a tridiagonal system of linear equations is presented. The new algorithm is shown to require reduced computational effort and have similar convergence and stability properties to the previous AGE scheme.
10 citations
TL;DR: It is proved that these matrices have at most two distinct tropical eigenvalues and the explicit formulas for those eigen values are given.
10 citations
TL;DR: A modification of Rojo's algorithm to solve block circulant tridiagonal systems of linear equations which are Toeplitz and Hermitian is presented, based on obtaining the solution of the nonlinear matrix equation [email protected]+B*@C^-^1B.
10 citations
19 Aug 1996
TL;DR: The optimal array processor improves the previous systolic designs based on the widely used Gaussian elimination in term of numerical stability and the time-space complexity for VLSI implementation because of the absence of division operations.
Abstract: The design of parallel algorithms and architectures for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method circumvents the ordinary single-step division-free method by its greater numerical stability. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop first an innovative regular iterative algorithm, then a two-dimensional array processor by deriving a localized dependency graph of the algorithm and adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal architecture under linear scheduling. The optimal array processor improves the previous systolic designs based on the widely used Gaussian elimination in term of numerical stability and the time-space complexity for VLSI implementation because of the absence of division operations.
10 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |