Journal Article10.1080/00207169008803839
A recursive decoupling method for solving tridiagonal linear systems
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TL;DR: By the use of repeated partitioning of the matrix into (2 × 2) subsystems it is shown that the linear system can be recursively decoupled into an explicit form suitable for solving on parallel or vector computers.
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Abstract: In many numerical methods it is necessary to solve repeatedly tridiagonal linear systems of a certain form, i.e. diagonally dominant. By the use of repeated partitioning of the matrix into (2 × 2) subsystems it is shown that the linear system can be recursively decoupled into an explicit form suitable for solving on parallel or vector computers.
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Citations
Explicit inverse of a generalized Vandermonde matrix
TL;DR: In this paper the author gives an explicit closed form expression for the nxn inverse matrix (V"G^(^k^)(n))^-^1 of the generalized nxN Vandermonde matrix V"G(^ k^)( n) by using the elementary symmetric functions.
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The parallel recursive decoupling algorithm for solving tridiagonal linear systems
G. Spaletta,David J. Evans +1 more
- 01 May 1993
TL;DR: It is shown, in fact, that the Recursive Decoupling method is intrinsically parallel and can be implemented as an efficient parallel algorithm.
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Inversion Of A Generalized Vandermonde Matrix
TL;DR: In this paper the author gives an explicit closed form expression for the inverse matrix $(V_{G}^{(k)})^{-1}(n)$ of the Vandermonde matrix (n) by using the elementary symmetric functions.
9
A note on the recursive decoupling method for solving tridiagonal linear systems
TL;DR: A new method to solve a tridiagonal linear system based on a rank-one updating strategy and the repeated partitioning of the coefficient matrix is described.
9
References
The solution of two-point boundary value problems by the alternating group explicit (AGE) method
David J. Evans,W. S. Yousif +1 more
TL;DR: In this paper, a new explicit iterative solution for the finite difference equations of the two-point boundary value problem is given, where the coefficient matrix of the obtained system is split into component matrices, and an iterative method formulated which can be easily expressed in explicit form is given.
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