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 Aug 1995
TL;DR: In this article, the authors studied nonsymmetric tridiagonal operators acting in the Hilbert space and described the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolute.
Abstract: We study nonsymmetric tridiagonal operators acting in the Hilbert space ?2 and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Pade approximants and spectral properties of nonsymmetric tridiagonal operators.
36 citations
TL;DR: In this paper, an efficient algorithm for the inversion of symmetric tridiagonal matrices is presented. But the algorithm is not suitable for the problem of computing the motion of charged particles in bubble chambers.
Abstract: EFFICIENT algorithms for the inversion of symmetric tridiagonal matrices are obtained. The results were published in [1]. Tridiagonal matrices are used not only in the application of finite difference methods to boundary value problems for second-order differential equations [2], but also in the solution of problems of nuclear physics [3]. Hence there is great interest in economical methods for the inversion of highorder band matrices by computer. In this paper efficient algorithms for the inversion of symmetric tridiagonal matrices are obtained. The methods of inversion obtained are compared with other methods. The theorem proved is useful for the solution in analytic form of the problem of processing physical information about the motion of charged particles in bubble chambers [4].
35 citations
TL;DR: In this article, the finite-difference patch-adaptive strategy for electrochemical kinetic simulations is extended to time-dependent models in one-dimensional space geometry, involving spatially localised unknowns at the boundaries, multiple space intervals, and non-local boundary conditions.
35 citations
TL;DR: In this paper, the facial structure of the polytope Ω t n in R n×n consisting of the tridiagonal doubly stochastic matrices of order n was studied.
35 citations
TL;DR: In this paper, the structure of inverses of nonsingular and irreducible tridiagonal matrices is reviewed and explicit inversion formulas are given for certain, not necessarily symmetric, tridimensional matrices.
Abstract: This paper first reviews some results on the structure of inverses of nonsingular and irreducible tridiagonal matrices. Next, explicit inversion formulas are given for certain, not necessarily symmetric, tridiagonal matrices. The results are then applied to matrices arising from discretization of two-point boundary value problems of the Sturm-Liouville type. The results show harmonic relations between the Green functions and the discrete Green functions for the problems. Finally the results are extended to block tridiagonal matrices. This work was supported by Scientific Research Grant-in-Aid from JSPS.
35 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |