FAST PARALLEL LINEAR EQUATION SOLVERS BASED ON TEXTURED DECOMPOSITION.

Garng Morton Huang, W. K. Tsai, W. Lu

Research output: Contribution to journalConference article

6 Citations (Scopus)

Abstract

A fast linear equation solver based on recursive textured decompositions is introduced. The computational time complexity for solving problems of N unknown variables is on the order of one if N processors are available. It is faster than the multigrid method, which, to date, was the fastest known method for two-dimensional Poisson equation, and which has time complexity of O(log N). The basic difference between this approach, and classical iterative algorithms, is that different approximations of the system matrix are used in round-robin fashion while one fixed approximation is used in the classical approach. It is shown that, with proper choice of approximation compositions, the spectral radius of error dynamic is reduced drastically; and with proper decomposition size, the spectral radius will approach a constant strictly less than one, even if the dimension of the problem tends to infinity. This enables a parallel algorithm with order-one time complexity to be derived.

Original languageEnglish
Pages (from-to)1450-1454
Number of pages5
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - 1 Dec 1987
Externally publishedYes

Fingerprint

Linear equations
Time Complexity
Linear equation
Spectral Radius
Decomposition
Decompose
Poisson equation
Approximation
Parallel algorithms
Multigrid Method
Poisson's equation
Parallel Algorithms
Iterative Algorithm
Computational Complexity
Strictly
Chemical analysis
Infinity
Tend
Unknown

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

FAST PARALLEL LINEAR EQUATION SOLVERS BASED ON TEXTURED DECOMPOSITION. / Huang, Garng Morton; Tsai, W. K.; Lu, W.

In: Proceedings of the IEEE Conference on Decision and Control, 01.12.1987, p. 1450-1454.

Research output: Contribution to journalConference article

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