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: The first polynomial-time algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices is given.
4 citations
TL;DR: A fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric andtridiagonal-Toeplitz systems, is presented, Employing the diagonally dominant property, the parallel solver does need only local communications between adjacent processors on a ring network.
Abstract: The solution of special linear, circulant-tridiagonal systems is considered. In this paper, a fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric and tridiagonal-Toeplitz systems, is presented. Employing the diagonally dominant property, our parallel solver does need only local communications between adjacent processors on a ring network. An error analysis is also given. On the nCUBE/2E multiprocessors, some experimental results demonstrate the good performance of our stable parallel solver.
4 citations
TL;DR: In this paper, the Lanczos method with an additional complete "forced" orthonormalization was shown to give perfect results even for high-order matrices, and an analytic formula for the eigenvectors was derived.
Abstract: Abstract Numerical methods for constructing symmetric tridiagonal matrices with prescribed distinct eigenvalues are studied. The first components of orthonormal eigenvectors or Symmetry* conditions are additionally given. An analytic formula for the eigenvectors is derived. Using numerical examples we show that the Lanczos method with an additional complete 'forced' orthonormalization gives perfect results even for high-order matrices. Without the additional complete 'forced' orthonormalization, good results are obtained for low-order matrices only. An algorithm for calculating the system of discrete orthogonal polynomials with arbitrary weight is proposed.
4 citations
Proceedings Article•
1 Jan 1993
4 citations
TL;DR: Another proof of Pell identities is presented by using the determinant of tridiagonal matrix via the Laplace expansion to calculate the Pell identities.
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |