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 Dec 2011
TL;DR: It is shown that in most cases MR^3-SMP is faster and achieves better speedups than state-of-the-art eigensolvers for uni-processors and distributed-memory systems.
Abstract: The computation of eigenvalues and eigenvectors of symmetric tridiagonal matrices arises frequently in applications; often as one of the steps in the solution of Hermitian and symmetric eigenproblems. While several accurate and efficient methods for the tridiagonal eigenproblem exist, their corresponding implementations usually target uni-processors or large distributed memory systems. Our new eigensolver MR^3-SMP is instead specifically designed for multi-core and many-core general purpose processors, which today have effectively replaced uni-processors. We show that in most cases MR^3-SMP is faster and achieves better speedups than state-of-the-art eigensolvers for uni-processors and distributed-memory systems.
16 citations
TL;DR: In this article, a tridiagonal matrix representation of the Dirac wave operator was used to find exact solutions of the one-dimensional Dirac equation using the tridimensional matrix representation, which made the wave equation equivalent to a symmetric three-term recursion relation for the expansion coefficients.
16 citations
TL;DR: This paper presents an extension of Rimas' work, deriving a similar expression for the entries of the qth power of the n × n Hermitian tridiagonal matrix tridiag n for all n ∈ N.
16 citations
TL;DR: The algorithm presented here works by eliminating all off-diagonal variables in terms of the diagonal ones, and then specifying values for the diagonal variables for tridiagonal problems in n steps for an n-origin, n-destination problem.
Abstract: Some transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, whil...
15 citations
TL;DR: A complex factorization formula for generalized fibonacci-Pell numbers obeying also classical Fibonacci and Pell numbers is obtained.
15 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |