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, the standard method of Gaussian elimination for the solution of linear algebraic equations is shown, with the aid of the concept of the factor or quotient space, to have a geometrical interpretation.
Abstract: The standard method of Gaussian elimination for the solution of linear algebraic equations is shown, with the aid of the concept of the factor or quotient space, to have a geometrical interpretation. This suggests alternative methods for the solution of equations of this type, and two new methods are described.
3 citations
TL;DR: In this paper, a fitting factor in the Galerkin difference scheme is introduced to take care of the rapid changes occur that in the boundary layer, which is obtained from the theory of singular perturbations.
Abstract: In this paper, we have presented a fitted Galerkin method for singularly perturbed differential equations with layer behaviour. We have introduced a fitting factor in the Galerkin difference scheme which takes care of the rapid changes occur that in the boundary layer. This fitting factor is obtained from the theory of singular perturbations. Thomas algorithm is used to solve the tridiagonal system of the fitted Galerkin method. The existence and uniqueness of the discrete problem along with stability estimates are discussed. Also we have discussed the convergence of the method. Maximum absolute errors in numerical results are presented to illustrate the proposed method.
3 citations
TL;DR: A similar algorithm for computing eigenvalues of skew-symmetric matrices, which is based on implicit usage of both the QR and the symplectic QR factorizations is constructed, and if applied to tridiagonal skew-SymmetricMatrices, this algorithm also enjoys high relative stability.
Abstract: Differential qd (dqd) algorithm with shifts is probably the fastest known algorithm which computes eigenvalues of symmetric tridiagonal matrices with high relative accuracy.
In this paper we will construct a similar algorithm for computing eigenvalues of skew-symmetric matrices, which is based on implicit usage of both the QR and the symplectic QR factorizations. If we apply this algorithm to tridiagonal skew-symmetric matrices, we obtain the skew-symmetric dqd algorithm. This algorithm also enjoys high relative stability. However, incorporation of shifts is much harder then in the symmetric case, and yet to be implemented.
Finally, the standard algorithm for computing the eigenvalues of tridiagonal skew-symmetric matrices can also be interpreted in the context of the skew-symmetric dqd algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
3 citations
TL;DR: In this paper, the authors considered tridiagonal matrices for which the main diagonal consists of zeros, the sup-diagonal of all ones, and the entries on the subdiagonal form a geometric progression, and established the criterion for the numerical range of such matrices to have line segments on its boundary.
Abstract: Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described.
3 citations
TL;DR: An explicit block tridiagonal solver suitable for parallel implementation is described for the equations derived from finite element discretisation of a two-point boundary value problem.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |