## Intrinsic parametrization for approximation.(English)Zbl 0644.65011

Let $$P_ i$$ $$(i=1(1)n)$$ be n given points. If this set of points is parametrized by a parameter $$t_ i$$, the approximation curve $Y(t)=\sum^{n}_{i=0}b_ if_ i(t)\quad (t\in I,\quad I=[a,b])\quad (n+1<N)$ with prescribed basis functions $$f_ i$$ is called optimal if the shortest distances between the points $$P_ i$$ and the approximation curve Y(t) is minimized.
An iterative Newton-like approach of intrinsic parametrization for the optimal approximation is proposed. The method is extended to optimal approximation surface of a given set of points $$P_{ik}$$ parametrized by parameter values $$(u_ i,v_ k)$$.
Reviewer: L.Gatteschi

### MSC:

 65D15 Algorithms for approximation of functions 53A04 Curves in Euclidean and related spaces 53A05 Surfaces in Euclidean and related spaces
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### References:

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