论文标题
最小二乘拟合的异步渐进式迭代近似法
Asynchronous progressive iterative approximation method for least-squares fitting
论文作者
论文摘要
对于大规模的数据拟合，Lin等人提出了最小二乘进行性的近似（LSPIA）方法。 （《暹罗科学计算杂志》，2013，35（6）：A3052-A3068）和Deng等。 （计算机辅助设计，2014，47：32-44），其中使用了恒定的步骤尺寸。在这项工作中，我们在Chebyshev半数方案的意义上进一步加速了LSPIA方法，并提出了异步LSPIA（ALSPIA）方法以适合数据点。 Alspia中的控制点通过利用外推变式进行更新，并根据Chebyshev多项式的根源选择自适应步长。我们的收敛性分析表明，在奇异和非发挥最小二乘配件的情况下，ALSPIA比原始LSPIA方法快。数值示例表明，所提出的算法是可行且有效的。
For large-scale data fitting, the least-squares progressive-iterative approximation (LSPIA) methods were proposed by Lin et al. (SIAM Journal on Scientific Computing, 2013, 35(6):A3052-A3068) and Deng et al. (Computer-Aided Design, 2014, 47:32-44), where the constant step sizes were used. In this work, we further accelerate the LSPIA method in the sense of a Chebyshev semi-iterative scheme and present an asynchronous LSPIA (ALSPIA) method to fit data points. The control points in ALSPIA are updated by utilizing an extrapolated variant and an adaptive step size is chosen according to the roots of Chebyshev polynomials. Our convergence analysis reveals that ALSPIA is faster than the original LSPIA method in both cases of singular and nonsingular least-squares fittings. Numerical examples show that the proposed algorithm is feasible and effective.
