### Abstract

Fast linear equation solvers based on recursive multiplicative, additive textured decompositions and corresponding recursive block Jacobi methods are introduced. The basic difference between this approach and classical iterative algorithms is that different approximations of the system matrix are used in the classical approach. It is shown that, with proper composition of approximation matrices, the spectral radius of error dynamic is greatly reduced, 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 inifinity. This enables the authors to devise a parallel algorithm with better time complexity. The associated recursive block Jacobi methods are developed and investigated, and their performance is compared with that of the textured decomposition methods. These algorithms are applied to dynamic simulation of parabolic equations.

Original language | English |
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Pages (from-to) | 1472-1477 |

Number of pages | 6 |

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

Publication status | Published - 1 Dec 1988 |

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*, 1472-1477.

**Fast parallel textured algorithms for parabolic equations.** / 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. 1472-1477.

}

TY - JOUR

T1 - Fast parallel textured algorithms for parabolic equations

AU - Huang, Garng Morton

AU - Tsai, W. K.

AU - Lu, W.

PY - 1988/12/1

Y1 - 1988/12/1

N2 - Fast linear equation solvers based on recursive multiplicative, additive textured decompositions and corresponding recursive block Jacobi methods are introduced. The basic difference between this approach and classical iterative algorithms is that different approximations of the system matrix are used in the classical approach. It is shown that, with proper composition of approximation matrices, the spectral radius of error dynamic is greatly reduced, 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 inifinity. This enables the authors to devise a parallel algorithm with better time complexity. The associated recursive block Jacobi methods are developed and investigated, and their performance is compared with that of the textured decomposition methods. These algorithms are applied to dynamic simulation of parabolic equations.

AB - Fast linear equation solvers based on recursive multiplicative, additive textured decompositions and corresponding recursive block Jacobi methods are introduced. The basic difference between this approach and classical iterative algorithms is that different approximations of the system matrix are used in the classical approach. It is shown that, with proper composition of approximation matrices, the spectral radius of error dynamic is greatly reduced, 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 inifinity. This enables the authors to devise a parallel algorithm with better time complexity. The associated recursive block Jacobi methods are developed and investigated, and their performance is compared with that of the textured decomposition methods. These algorithms are applied to dynamic simulation of parabolic equations.

UR - http://www.scopus.com/inward/record.url?scp=0024175886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024175886&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0024175886

SP - 1472

EP - 1477

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -