## Best interpolation with free nodes by closed curves.(English)Zbl 0675.41008

Mathematical methods in computer aided geometric design, Pap. Int. Conf., Oslo/Norw. 1988, 549-559 (1989).
Summary: [For the entire collection see Zbl 0669.00011.]
Best interpolation with free nodes addresses the problem of designing a curve through prescribed points in $${\mathbb{R}}^ d$$ such that some smoothness functional is minimized; e.g., the $$k^{th}$$ derivative in the least square sense. In addition the nodes are allowed to vary freely. Here we consider closed curves. We prove existence of an optimal curve in the general case and uniqueness in the cubic case $$k=2$$.

### MSC:

 41A05 Interpolation in approximation theory

### Keywords:

Best interpolation; optimal curve

Zbl 0669.00011