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 article, a general method for mathematical simulation of multicomponent equilibrium stage processes is presented, which consists of solving component material balance equations with a tridiagonal matrix algorithm and performing equilibrium calculation based on the "pseudoequilibrium" concept, instead of solving simultaneous equilibrium equations by some optimization method.
Abstract: A new general method for mathematical simulation of multicomponent equilibrium stage processes is presented. The procedure consists of solving component material balance equations with a tridiagonal matrix algorithm and performing equilibrium calculation based on the "pseudoequilibrium" concept, instead of solving simultaneous equilibrium equations by some optimization method. The present method is simple, fast and numerically stable. The application of the method to multistage, multicomponent extraction problems is described. Moreover, the feasibility of the modified Wilson equation to extraction problems is shown.
17 citations
1 Apr 1992
TL;DR: The weaker error bound of QR as implemented in LAPACK's SSTEQR or EISPACK's IMTQL is shown to be unavoidable, by presenting a particular symmetric positive de nite tridiagonal matrix for which QR must fail, given any reasonable shift strategy.
Abstract: Recently Demmel and Veselic showed that Jacobi's method has a tighter relative error bound for the computed eigenvalues of a symmetric positive de nite matrix than does QR iteration. Here we show the weaker error bound of QR as implemented in LAPACK's SSTEQR or EISPACK's IMTQL is unavoidable. We do this by presenting a particular symmetric positive de nite tridiagonal matrix for which QR must fail, given any reasonable shift strategy.
17 citations
TL;DR: This paper relates disconjugacy of linear Hamiltonian difference systems (LHdS) (and hence positive definiteness of certain discrete quadratic functionals) to positive definIteness of some block tridiagonal matrices associated with these systems and functionals.
Abstract: This paper relates disconjugacy of linear Hamiltonian difference systems (LHdS) (and hence positive definiteness of certain discrete quadratic functionals) to positive definiteness of some block tridiagonal matrices associated with these systems and functionals. As a special case of a Hamiltonian system, Sturm--Liouville difference equations are considered, and analogous results are obtained for these important objects.
16 citations
TL;DR: A fitted fourth-order tridiagonal finite difference scheme for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point is presented.
16 citations
TL;DR: In this paper, it is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx = b, whereb is nonnegative, with small entrywise relative error.
Abstract: This paper establishes a new entrywise relative perturbation result for the inverse of a nonsingularM-matrixA. It is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx =b, whereb is nonnegative, with small entrywise relative error. IfA is tridiagonal, the Gaussian elimination alone suffices.
16 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |