• 论文 •

### 两类向量序列加速收敛方法比较

1. 1. 中国工程物理研究院研究生院, 北京 100088;
2. 北京应用物理与计算数学研究所, 计算物理重点实验室, 北京 100094;
3. 中物院高性能数值模拟软件中心, 北京 100088;
4. 东北师范大学, 数学与统计学院, 长春 130024
• 收稿日期:2020-10-09 出版日期:2021-12-15 发布日期:2021-12-07
• 基金资助:
国家重点研发计划（2017YFA0603903）和国家自然科学基金（12171045，11671051）资助.

Qin Zikang, An Hengbin, Wang Xinyu. COMPARISON OF TWO METHODS FOR ACCELERATING CONVERGENCE OF VECTOR SEQUENCES[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(4): 379-394.

### COMPARISON OF TWO METHODS FOR ACCELERATING CONVERGENCE OF VECTOR SEQUENCES

Qin Zikang1, An Hengbin2,3, Wang Xinyu4

1. 1. Graduate School of CAEP, Beijing 100088, China;
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
3. CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China;
4. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
• Received:2020-10-09 Online:2021-12-15 Published:2021-12-07

The iterative algorithms are the main methods for solving large scale linear and nonlinear problems. The convergence rate of the vector sequences produced by an iterative method has direct influence on the application effectiveness. To improve the convergence rate of a vector sequence, an iterative acceleration algorithm may be employed. Currently, there are mainly two classes of iterative acceleration algorithms:One is the extrapolation methods and the other is Anderson acceleration method. In an extrapolation method, a new vector sequence is obtained by transforming the original vector sequence, such that the new vector sequence converges faster than the original sequence. The typical extrapolation algorithms include minimal polynomial extrapolation (MPE) algorithm, modified minimal polynomial extrapolation (MMPE) algorithm, reduced rank extrapolation (RRE) algorithm, topological ε-algorithm (TEA), and vector ε-algorithm (VEA). Anderson acceleration is designed for fixed point iteration, where the new sequence is constructed by employing the information of the history residual vectors. In this paper, RRE algorithm, which is chosen as a representative of the extrapolation algorithms, is compared with Anderson acceleration algorithm. The emphasis of the comparison is on the numerical tests and analysis for several typical applications. The results show that both of the algorithms can improve the convergence rate of the iterative sequence, and Anderson acceleration algorithm is more robust and efficient than RRE algorithm.

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