Fitting Parametric Curves and Surfaces by l∞ Distance Regression
Fitting Parametric Curves and Surfaces by l∞ Distance Regression
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DOI：
10.1007/s10543-005-0018-z
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发表时间：
2005-09
影响因子：
1.5
通讯作者：
I. Al-Subaihi;G. Watson
中科院分区：
文献类型：
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作者：
I. Al-Subaihi;G. Watson
对于将曲线或曲面拟合到观察或测量数据，常用的准则是正交距离回归。我们认为在这里一个自然的推广的一个特定的配方，涉及到更换最小二乘的切比雪夫规范的问题。例如，该标准在制造零件的接受/拒绝决策的上下文中可能是更合适的标准。由此产生的问题有一些有趣的特点：它有很多可以利用的结构，但通常解决方案不是唯一的。我们考虑一种方法的高斯-牛顿型，并表明，如果解决的非唯一性的方式是一致的，这是一个特定的方式利用结构的线性子问题，这不仅可以允许该方法被适当地定义，但可以允许二阶收敛速度。给出数值例子来说明这一点。
For fitting curves or surfaces to observed or measured data, a common criterion is orthogonal distance regression. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of least squares by the Chebyshev norm. For example, this criterion may be a more appropriate one in the context of accept/reject decisions for manufactured parts. The resulting problem has some interesting features: it has much structure which can be exploited, but generally the solution is not unique. We consider a method of Gauss-Newton type and show that if the non-uniqueness is resolved in a way which is consistent with a particular way of exploiting the structure in the linear subproblem, this can not only allow the method to be properly defined, but can permit a second order rate of convergence. Numerical examples are given to illustrate this.