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
Journal Article•
TL;DR: In this paper, inversion of periodic tridiagonal matrices is discussed using the t vector and the algorithm has a low computational cost as well as high precision.
Abstract: In this paper,inversion of periodic tridiagonal matrices is discussed using the t vector.Computational complexity of the inversion is 2n2+O(n)of multiplication and division and n2+O(n)of addition and subtraction.The algorithm has a low computational cost as well as high precision.The computational cost is further reduced to become proportional to nif the t vector is truncated and fast inversed.In contrast to the existing fast algorithms,the out-of-memory errors no longer occur.Numerical examples are presented.
2 citations
Journal Article•
TL;DR: In this paper, an algorithm for inverting a tridiaognal matrix and the explicit expression of the elements of the inverse matrix are presented. But the complexity and the computing time of this algorithm is lower than those of some existing algorithms for invertering a block tridia-ognal matrices.
Abstract: In this paper,the inverse of a tridiagonal matrix is investigated.By the LU and UL decompositions of a tridiagonal matrix and the special structure of the inverse matrix,an algorithm for inverting a tridiaognal matrix and the explicit expression of the elements of the inverse matrix are presented.The computing complexity and the computing time of this algorithm is lower than those of some existed algorithms for inverting a block tridiaognal matrix.
2 citations
28 Dec 2010
TL;DR: A Newton-Krylov type algorithm is designed and implemented for a pseudo compressible Navier-Stokes solver in an incompressible Cavity flow showing promising convergence acceleration especially for the GMRES/ILU-1 case compared to the classic Approximate Factorization method.
Abstract: A Newton-Krylov type algorithm is designed and implemented for a pseudo compressible Navier-Stokes solver in an incompressible Cavity flow. Both GMRES and BICGSTAB (Krylov-subspace) techniques are employed for the solving the linear solver resulting from the residual linearization. ILU-0 and ILU-1 and Thomas algorithm are used for preconditioning. The results show promising convergence acceleration especially for the GMRES/ILU-1 case compared to the classic Approximate Factorization method.Copyright © 2010 by ASME
2 citations
TL;DR: In this paper, it was shown that the number of real roots of a polynomial given by a tridiagonal determinantal representation is greater than the signature of this representation.
2 citations
1 Jan 1984
TL;DR: In this article, it was shown that the intermediate equations of Gaussian elimination are related to rational interpolating functions that depend on subsets of the coefficients and data, and that the procedure breaks down only if r(ξ) or the coefficients of the rational function are not properly defined.
Abstract: We consider the calculation of r(ξ), where ξ is a given number, and where {r(x)=p(x)/q(x); xe IR} is a generalized rational function whose coefficients should satisfy some interpolation conditions. We study a procedure that obtains r(ξ)=p(ξ)/q(ξ) by applying Gaussian elimination to remove the unknown coefficients from a system of linear equations. It is shown that the procedure breaks down only if r(ξ) or the coefficients of the rational function are not properly defined. It is proved that the intermediate equations of Gaussian elimination are related to rational interpolating functions that depend on subsets of the coefficients and data. A numerical example demonstrates the procedure.
2 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |