Journal Article10.1016/0167-8191(93)90006-7
The parallel recursive decoupling algorithm for solving tridiagonal linear systems
G. Spaletta,David J. Evans +1 more
- 01 May 1993
- Vol. 19, Iss: 5, pp 563-576
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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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Abstract: In this paper we describe a new tridiagonal equation solver, based on a rank-one updating strategy and the repeated partitioning of the system matrix into 2 × 2 submatrices. On this basis, a recursive decoupling method is developed [2,3], which operates on the tridiagonal linear system, enabling the solution to be expressed in explicit form and solved independently on a multiprocessor system. We will show, in fact, that the Recursive Decoupling method is intrinsically parallel and can be implemented as an efficient parallel algorithm.
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Citations
Manycore Algorithms for Batch Scalar and Block Tridiagonal Solvers
TL;DR: This work investigates the optimal choice of tridiagonal algorithm for CPU, Intel MIC, and NVIDIA GPU with a focus on minimizing the amount of data transfer to and from the main memory using novel algorithms and the register-blocking mechanism, and maximizing the achieved bandwidth.
Unified architecture for divide and conquer based tridiagonal system solvers
TL;DR: It is concluded that the constant geometry Cyclic Reduction architecture is the most appropriate one for solving tridiagonal systems and, from the point of view of integration in VLSI technology, is the one which uses the least amount of area and the smallest number of pins.
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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.
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•Dissertation
Design and evaluation of tridiagonal solvers for vector and parallel computers
Larriba Pey,Josep Lluís +1 more
- 10 Mar 1995
TL;DR: In this paper, the authors discuss the resolution of SISTEMAS TRIDIAGONALES DE ECUACIONES in the context of a new metoda.
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A practical and portable model of programming for iterative solvers on distributed memory machines
Samuel Kortas,Philippe Angot +1 more
- 01 Jun 1996
TL;DR: A practical and portable model of parallel programming inspired from the systolic handling of array shift on SIMD machines is presented, where all the communications are hidden to the user who can code parallel iterative solvers in a more natural way on MIMD machines.
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References
•Book
A collection of matrices for testing computational algorithms
Robert Todd Gregory,David L. Karney +1 more
- 01 Jan 1969
305
A Parallel Method for Tridiagonal Equations
TL;DR: A new (partition) method for solving a tndiagonal system of lmear equations is presented and various situations under which the partmon method can be preferable are described.
A recursive decoupling method for solving tridiagonal linear systems
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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•Dissertation
The recursive decoupling method for solving tridiagonal linear systems
Giulia Spaletta
- 01 Jan 1991
TL;DR: The work presented in this thesis mainly concerns the analysis of parallel algorithms for the solution of tridiagonal linear systems and the design of a newtridiagonal equation solver, which can be run on a MIMD type parallel computer, in particular the Balance 8000 Sequent system at Loughborough University of Technology.
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