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
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Papers
TL;DR: A first-order non-conforming numerical methodology, separation method, for fluid flow problems with a 3-point exponential interpolation scheme has been developed and it is shown that the traditional upwind scheme is less than first- order-accuracy.
Abstract: A first-order non-conforming numerical methodology, separation method, for fluid flow problems with a 3-point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one-dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first-order-accurate. The discretisation of each one-dimensional subproblem is based on a 3-point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first-order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first-order-accuracy. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri-diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square-driven cavity. The convergence rates are compared with the traditional schemes for the square-driven cavity problem. Good behaviour of the proposed scheme is ascertained.
TL;DR: It turns out that a combination of the Thomas algorithm and the approximate inverse leads to a solution that does not need either tiling or transpositions, and none of the kernels uses an extensive amount of shared memory which yields a very high GPU utilization and more importantly optimal coalesced global memory access patterns.
TL;DR: The estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices are given.
Abstract: The theory and method of matrix computation, as an important tool, have much important applications such as in computational mathematics, physics, image processing and recognition, missile system design, rotor bearing system, nonlinear kinetics, economics and biology etc. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal period matrices.
TL;DR: This paper presents an algorithm for computing any block of the inverse of a block tridiagonal, nearly block Toeplitz matrix that scales independently of the total number of blocks in the matrix and linearly with the number of deviations.
Abstract: We present an algorithm for computing any block of the inverse of a block tridiagonal, nearly block Toeplitz matrix (defined as a block tridiagonal matrix with a small number of deviations from the purely block Toeplitz structure). By exploiting both the block tridiagonal and the nearly block Toeplitz structures, this method scales independently of the total number of blocks in the matrix and linearly with the number of deviations. Numerical studies demonstrate this scaling and the advantages of our method over alternatives.
TL;DR: A parallel variant of the block Gauss–Seidel iteration is presented for the solution of block tridiagonal linear systems and parallel computations derive from a block reordering of the blocks.
Abstract: A parallel variant of the block Gauss–Seidel iteration is presented for the solution of block tridiagonal linear systems. In this method parallel computations derive from a block reordering of the ...
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |