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: In this paper, the authors obtained an explicit expression for the spectral matrix measure corresponding to the associated doubly infinite tridiagonal matrix in the Jacobi case, restoring the simplicity of the familiar orthogonality relations satisfied by Jacobi polynomials.
Abstract: The associated Hermite, Laguerre, Jacobi, and Bessel polynomials appear naturally when Bochner's problem [5] of characterizing orthogonal polynomials satisfying a second-order differential equation is extended to doubly infinite tridiagonal matrices. We obtain an explicit expression for the spectral matrix measure corresponding to the associated doubly infinite tridiagonal matrix in the Jacobi case. We show that, in an appropriate basis of \"bispectral\" functions, the spectral matrix can be put into a nice diagonal form, restoring the simplicity of the familiar orthogonality relations satisfied by the Jacobi polynomials.
14 citations
TL;DR: This paper presents a linear time algorithm for checking whether a tridiagonal matrix will become singular under certain perturbations of its coefficients, which is known to be NP-hard for general matrices.
Abstract: In this paper we present a linear time algorithm for checking whether a tridiagonal matrix will become singular under certain perturbations of its coefficients The problem is known to be NP-hard for general matrices Our algorithm can be used to get perturbation bounds on the solutions to tridiagonal systems
14 citations
1 Aug 1966
TL;DR: Two tested programs are supplied to find the eigenvalues of a symmetric tridiagonal matrix using a square-root-free version of the QR algorithm and a compact kind of Sturm sequence algorithm.
Abstract: Two tested programs are supplied to find the eigenvalues of a symmetric tridiagonal matrix. One program uses a square-root-free version of the QR algorithm. The other uses a compact kind of Sturm sequence algorithm. These programs are faster and more accurate than the other comparable programs published previously with which they have been compared.
14 citations
Posted Content•
TL;DR: This paper uses a connection between their eigenvalues and zeros of appropriate matrix polynomials to derive a closed-form expression for the eigenvectors of block tridiagonal matrices, which eliminates the need for their direct calculation and can lead to a faster calculation of eigen values.
Abstract: Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large matrix sizes. In this paper, we address the problem of the eigendecomposition of block tridiagonal matrices by studying a connection between their eigenvalues and zeros of appropriate matrix polynomials. We use this connection with matrix polynomials to derive a closed-form expression for the eigenvectors of block tridiagonal matrices, which eliminates the need for their direct calculation and can lead to a faster calculation of eigenvalues. We also demonstrate with an example that our work can lead to fast algorithms for the eigenvector expansion for block tridiagonal matrices.
14 citations
TL;DR: By the use of repeated partitioning of the matrix into (2 × 2) subsystems it is shown that the linear system can be recursively decoupled into an explicit form suitable for solving on parallel or vector computers.
Abstract: In many numerical methods it is necessary to solve repeatedly tridiagonal linear systems of a certain form, i.e. diagonally dominant. By the use of repeated partitioning of the matrix into (2 × 2) subsystems it is shown that the linear system can be recursively decoupled into an explicit form suitable for solving on parallel or vector computers.
14 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |