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: Brownian matrices arise in certain models used in digital signal processing as discussed by the authors and can be used to solve linear systems of linear equations, where any brownian matrix is congruent to a tridiagonal matrix.
Abstract: Brownian matrices arise in certain models used in digital signal processing. Fast algorithms for solving brownian systems of linear equations can be derived because any brownian matrix is congruent to a tridiagonal matrix. This, and related properties, are developed and extended to matrices having a more general patterned structure.
15 citations
TL;DR: In this paper, the relation between the determinant and Chebyshev polynomials was studied in terms of k-balancing number, which generalizes some well known results concerning the relation of determinant polynomial and Chebyhev Polynomial, due to tridiagonal matrix B(n)(k).
Abstract: In this paper, we give some relations in terms of k- Balancing number which generalize some well known results concerning the relation between the determinant and Chebyshev polynomials which is due to tridiagonal matrix B(n)(k). Also for the other tridiagonal matrix W(n)(k); we deduce the cofactor matrix of it then we nd another relations for k- Balancing number.
15 citations
TL;DR: In this paper, the authors discuss the application of an implicit scheme to the solution by finite differences of transient natural convection in terms of the stream function and temperature, and verify the hypothesis and the algorithm using the transient NN solution in the following parameter ranges: 10 3 r Ra r 10 6, 10 -2 r Pr r 10 2, 21 2 21 r grid r 61 2 61.
Abstract: In this article we discuss the application of an implicit scheme to the solution by finite differences of transient natural convection in terms of the stream function and temperature. The second-order energy differential and fourth-order momentum equations are discretized according to the well-known alternate direction implicit (ADI) method. Then the temperature field solution is built based on the classic tridiagonal matrix algorithm (TDMA), and the stream function solution is built based on the two original hypotheses proposed here together with the penta diagonal matrix algorithm (PDMA). The time step in the algorithm is obtained analytically as a function of the Prandtl number and the size of the grid imposing the diagonal dominance condition in the pentadiagonal matrix generated by the hypothesis. We verify the hypothesis and the algorithm using the transient natural convection solution in the following parameter ranges: 10 3 r Ra r 10 6 , 10 -2 r Pr r 10 2 , 21 2 21 r grid r 61 2 61. The transient s...
15 citations
TL;DR: In this article, the stability of the (1+1)-dimensional nonlinear Dirac equation was investigated using the Thomas algorithm in the matrix form, and it was proved that all of the schemes are unconditionally stable in the linear sense.
Abstract: In this work, a fourth-order in space and second-order in time compact scheme, a sixth-order in space and second-order in time compact scheme and two linearized compact schemes are proposed for the (1+1)-dimensional nonlinear Dirac equation. The iterative algorithm is used to compute the nonlinear algebraic system and the Thomas algorithm in the matrix form is adopted to enhance the computational efficiency. It is proved that all of the schemes are unconditionally stable in the linear sense. Numerical experiments are given to test the accuracy order of the presented schemes, record the error history for all of the schemes with respect to t, discuss the conservation laws of discrete charge and energy from the numerical point of view, study the stability of the solitary waves by adding a small random perturbation to the initial data, and simulate the collision of two and three solitary waves.
15 citations
TL;DR: It is shown that every n by n symmetry matrix over F is orthogonally similar to a tridiagonal symmetric matrix, if further the characteristic is 0.
15 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |