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 method for inverting tridiagonal matrices by adopting the strategy resulting in a recursive doubling algorithm is presented; the present algorithm has a highly parallel structure.
Abstract: Evans [2, 3] introduced the method of recursive point partitioning algorithm for the solution of sparse banded matrix systems and investigated the “one-line at a time” strategy for the solution of tridiagonal linear systems. Recursive block partitioning schemes resulting from variation in the size of the block structure using “two-lines at a time” have been investigated for both the tridiagonal and the quindiagonal matrix systems in Okolie [6]. The case of partitioning strategy for an nth order system has been considered by Evans and Okolie [4] resulting in a recursive decoupling algorithm for tridiagonal linear systems. Following the recursive point partitioning algorithm of Evans [2, 3], Chawla et al [1] developed a recursive partitioning algorithm for inverting tridiagonal matrices. In the present paper we present a method for inverting tridiagonal matrices by adopting the strategy resulting in a recursive doubling algorithm; the present algorithm has a highly parallel structure.
2 citations
TL;DR: In this article, explicit relations between the elements of the inverse of a quasi-tridiagonal matrix and its associated tridiagonal inverse were derived, assuming that the tridimensional inverse is known.
Abstract: Explicit relations are derived between the elements of the inverse of a quasi-tridiagonal matrix and the elements of the inverse of the associated tridiagonal matrix. These relations are used to compute the quasi-tridiagonal inverse assuming that the tridiagonal inverse is known.
2 citations
TL;DR: In this paper, the problem of bracketing the first eigenvalues of a tridiagonal matrix H is studied and sufficient conditions for lower bounds are given based on a low estimate of the characteristic limit.
Abstract: The problem of upper and lower bounds to the first few eigenvalues of a very large or infinite tridiagonal matrix H is studied. Those eigenvalues of a comparison-matrix Mn which are lower than a characteristic limit, together with the corresponding eigenvalues of the variational matrix Hn are shown to bracket exact eigenvalues of H. Mn differs from Hn only in the last off-diagonal element and is easily obtained from H. Sufficient conditions for lower bounds are based on a low estimate of the characteristic limit. For increasing dimensions n, the lower bounds approach the exact eigenvalues from below. As a numerical illustration, brackets to the known eigenvalues of the harmonic oscillator with a linear perturbation are calculated.
2 citations
TL;DR: In this paper, a two-phase method was proposed to solve a set of nonequilibrium material balance equations for liquid extractors and vapor absorbers. But it is applicable only to conventional distillation columns.
2 citations
Journal Article•
TL;DR: A new recursive algorithm is proposed for computing the inverse of a periodic tridiagonal matrix that can cut down the amount of calculation and storing capacity, and has some advangtages evidently in accuracy of the calculation.
Abstract: In this paper,a new recursive algorithm is proposed for computing the inverse of a periodic tridiagonal matrix.The new algorithm make the most of the special structure of the periodic tridiagonal matrix,by using the recursive computational method,a high-order periodic tridiagonal is transformed into a low-order periodic tridiagonal for computing the inverse.Then the simplified calculation method is obtained,it can cut down the amount of calculation and storing capacity,and it has some advangtages evidently in accuracy of the calculation.From the numerical experiments it has been known that the methods is effective.
2 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |