Preconditioned progressive iterative approximation for tensor product Said-Ball patches(张量积型Said-Ball曲面的预处理渐近迭代逼近法)

QUANHaorong(全浩荣); LIUChengzhi(刘成志); LIJuncheng(李军成); YANGLian(杨炼); HULijuan(胡丽娟)

doi:10.3785/j.issn.1008-9497.2022.06.006

Zhejiang Daxue xuebao. Lixue ban (Nov 2022)

Preconditioned progressive iterative approximation for tensor product Said-Ball patches(张量积型Said-Ball曲面的预处理渐近迭代逼近法)

QUANHaorong(全浩荣),
LIUChengzhi(刘成志),
LIJuncheng(李军成),
YANGLian(杨炼),
HULijuan(胡丽娟)

Affiliations

QUANHaorong(全浩荣): ORCiD; College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China(湖南人文科技学院　数学与金融学院，湖南　娄底　417000)
LIUChengzhi(刘成志): ORCiD
LIJuncheng(李军成): College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China(湖南人文科技学院　数学与金融学院，湖南　娄底　417000)
YANGLian(杨炼): College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China(湖南人文科技学院　数学与金融学院，湖南　娄底　417000)
HULijuan(胡丽娟): College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, Hunan Province, China(湖南人文科技学院　数学与金融学院，湖南　娄底　417000)

DOI: https://doi.org/10.3785/j.issn.1008-9497.2022.06.006
Journal volume & issue: Vol. 49, no. 6
pp. 682 – 690

Abstract

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为加快张量积型Said-Ball曲面渐近迭代逼近法的收敛速度，探讨了张量积型Said-Ball曲面渐近迭代逼近法的预处理技术。首先利用对角补偿约化技术构造了预处理子，然后结合矩阵Kronecker积性质，采取预处理渐近迭代逼近法求解张量积型Said-Ball曲面。为进一步降低计算量并提高算法的稳定性，利用广义极小残差法求解预处理方程，得到预处理渐近迭代逼近法的非精确求解方法。分析了预处理渐近迭代逼近法及非精确求解方法的收敛性。最后用数值实例说明预处理子能大大减小迭代矩阵的谱半径，令预处理技术及其非精确求解方法的计算效率明显提高。此外，由于对角补偿预处理子能改善配置矩阵的谱分布，因此也可用于对广义极小残差法的预处理，以改善其收敛性。

Published in Zhejiang Daxue xuebao. Lixue ban

ISSN: 1008-9497 (Print)
Publisher: Zhejiang University Press
Country of publisher: China
LCC subjects: Science: Mathematics: Instruments and machines: Electronic computers. Computer science; Science: Physics
Website: https://www.zjujournals.com/sci/EN/1008-9497/home.shtml

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