Chebyshev Periodical Successive Over-Relaxation for Accelerating Fixed-Point Iterations
Chebyshev Periodical Successive Over-Relaxation for Accelerating Fixed-Point Iterations
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DOI：
10.1109/lsp.2021.3073620
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发表时间：
2020-01
影响因子：
3.9
通讯作者：
T. Wadayama;Satoshi Takabe
中科院分区：
文献类型：
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作者：
T. Wadayama;Satoshi Takabe
提出了一种加快不动点迭代收敛速度的新方法——切比雪夫周期连续过松弛法。Chebyshev PSOR可以看作是利用Chebyshev多项式的根的逆作为迭代相关的PSOR因子的连续过松弛的一种变体。该方法最显著的特点之一是除了线性不动点迭代外，还可以应用于非线性不动点迭代。几个数值实验表明，Chebyshev PSOR对于包括近端梯度方法（如ISTA）在内的广泛类别的线性和非线性不动点迭代具有更快的收敛速度。
A novel method, termed Chebyshev periodical successive over-relaxation (PSOR), for accelerating the convergence speed of fixed-point iterations is presented. Chebyshev PSOR can be regarded as a variant of successive over-relaxation utilizing the inverse of roots of a Chebyshev polynomial as iteration-dependent PSOR factors. One of the most notable features of the proposed method is that it can be applied to nonlinear fixed-point iterations in addition to linear fixed-point iterations. From several numerical experiments, it is shown that Chebyshev PSOR leads to faster convergence for wide classes of linear and non-linear fixed-point iterations including proximal gradient methods such as ISTA.