论文标题
B-Spline曲线和表面配件的随机进行性迭代近似
Randomized progressive iterative approximation for B-spline curve and surface fittings
论文作者
论文摘要
对于大规模数据拟合，最小二乘进行性迭代近似是许多应用域中广泛使用的方法，因为其直观的几何含义和效率。在这项工作中，我们提出了B型曲线曲线和表面配件的随机进行性迭代近似（RPIA）。在每次迭代中，RPIA根据索引选择的随机标准在本地调整控制点。每个控制点的差异是关于随机块坐标下降法的计算。从几何和代数方面，提供了RPIA的插图。我们证明RPIA构建了一系列拟合曲线（分别，表面），其极限曲线（分别为，表面）可以将预期收敛到给定数据点的最小二乘拟合结果。进行数值实验以确认我们的结果并显示RPIA的好处。
For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive iterative approximation (RPIA) for the B-spline curve and surface fittings. In each iteration, RPIA locally adjusts the control points according to a random criterion of index selections. The difference for each control point is computed concerning the randomized block coordinate descent method. From geometric and algebraic aspects, the illustrations of RPIA are provided. We prove that RPIA constructs a series of fitting curves (resp., surfaces), whose limit curve (resp., surface) can converge in expectation to the least-squares fitting result of the given data points. Numerical experiments are given to confirm our results and show the benefits of RPIA.
