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 1989
TL;DR: In order to remove the factorization error en efficient nested iterative method, only tridiagonal matrix inversions are needed and amount of computation is much reduced at each time step.
Abstract: Algorithm for solving the difference equations is considered. The difference eq. obtained with approximate factorization for 3-D stable implicit schemes may become unstable or conditionally stable. If proper Jacobian matrix splitting is used stable approximately factored scheme can be obtained. In order to remove the factorization error en efficient nested iterative method is suggested. In this method only tridiagonal matrix inversions are needed. Amount of computation is much reduced at each time step.
1 citations
15 Apr 2002
TL;DR: The algorithms to be presented are based on projection methods for solving linear systems of equations with coefficient matrix assumed to be nonsingular tridiagonal and Toeplitz and can be solved in parallel with corrections to follow.
Abstract: The algorithms to be presented are based on projection methods for solving linear systems of equations. The coefficient matrix is assumed to be nonsingular tridiagonal and Toeplitz. Often such systems arise with a positive definite or diagonally dominant matrix. Through a set of perturbations, subsystems can be solved in parallel with corrections to follow.
1 citations
1 Mar 1984
TL;DR: This paper presents a divide-and-conquer approach to the evaluation of the characteristic polynomial of a symmetric tridiagonal matrix for a real argument and shows that the three-term recurrence is a specific case of the equations.
Abstract: In this paper, we present a divide-and-conquer approach to the evaluation of the characteristic polynomial of a symmetric tridiagonal matrix for a real argument. Here, the problem is partitioned into smaller parts which are solved and these solutions are then combined to form the solution to the original problem. We give the update equations for the characteristic polynomial and certain auxiliary polynomials used in the computation. We show that the three-term recurrence is a specific case of our equations. Furthermore, this set of recursions can be implemented on a regular tree structure. If the concurrency exhibited by order is increased by one at every step.
1 citations
TL;DR: A synthesis, procedure for tridiagonal state-space structures is presented that yields structures with a reduced number of multipliers and eliminates zero-input and constant-input limit cycles.
Abstract: A synthesis, procedure for tridiagonal state-space structures is presented that yields structures with a reduced number of multipliers and eliminates zero-input and constant-input limit cycles. The output roundoff noise is minimized by optimizing some free parameters. Some design examples are presented illustrating the synthesis procedure. >
1 citations
TL;DR: A more flexible process that selects a pivot for each nonzero to be eliminated and it is shown that recognizing matrices that allow such perfect partial elimination schemes is NP-hard.
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |