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 Jan 1995
TL;DR: In this article, the authors considered linear systems of algebraic equations with tridiagonal interval matrix S and interval vector f and presented estimates of the absolute value and the width of the intervals ui, i = 1, 2,...,, ~z tinder certain assumptions on the elements of the matrix S that do not include the traditional condition of diagonal dominance.
Abstract: We consider linear systems of algebraic equations Su = f with tridiagonal interval matrix S and interval vector f An interval version of the sweep method allows us to find an interval vector u = ( u t , u 2 , . . . , u n ) T that contains the united set of solutions of the system. In the paper we present estimates of the absolute value and the width of the intervals ui, i = 1, 2 , . . . , ~z tinder certain assumptions on the elements of the matrix S that do not include the traditional condition of diagonal dominance. The width estimates are three orders of magnitude narrnwer, and the assumptions on the system's coefficients are weaker than those in works published so far.
1 Oct 1990
TL;DR: The parallel numerical solution of the matrix eigenvalue problem for real symmetric tridiagonal matrices is discussed and two implementations of the Sturm sequence algorithm on transputer arrays are described.
Abstract: We discuss the parallel numerical solution of the matrix eigenvalue problem for real symmetric tridiagonal matrices. Instances occur frequently in practice. Two implementations of the Sturm sequence algorithm on transputer arrays are described. For the first the maximum size of matrices which may be accommodated is restricted by the amount of local memory available. The second implementation removes this constraint but requires an increased execution time.
TL;DR: An ALGOL program is derived for a modified LR-algorithm, permitting the determination of two-sided approximations to the eigenvalues of a tridiagonal symmetric matrix.
Abstract: An ALGOL program is derived for a modified LR-algorithm, permitting the determination of two-sided approximations to the eigenvalues of a tridiagonal symmetric matrix. Test examples are considered.
1 Jul 1999
TL;DR: The application of the conjugate gradient method specifically to solve non symmetric systems which are large, tridiagonal and Toeplitz, and to solve the pairs of systems using a parallel implementaton of congujate gradient.
Abstract: In this paper, we consider the application of the conjugate gradient method specifically to solve non symmetric systems which are large, tridiagonal and Toeplitz. Under the condition that the system is diagonally dominant, one can pre-multiply the system by the transpose of the coefficient matrix and take advantage of the structure of the new coefficient matrix to perturb and factor it. This allows us to divide the task of solution containing pairs of tridiagonal, symmetric and Toeplitz systems and to solve the pairs of systems using a parallel implementaton of congujate gradient. Final corrections, to account for the perturbations, provide a numerical approximation to the solution.
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |