### 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 language | English |
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Pages (from-to) | 1450-1454 |

Number of pages | 5 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Publication status | Published - 1 Dec 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*, 1450-1454.

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

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, pp. 1450-1454.

}

TY - JOUR

T1 - FAST PARALLEL LINEAR EQUATION SOLVERS BASED ON TEXTURED DECOMPOSITION.

AU - Huang, Garng Morton

AU - Tsai, W. K.

AU - Lu, W.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023541412&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023541412&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0023541412

SP - 1450

EP - 1454

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -