On uniqueness of best spline approximations with free knots
نویسندگان
چکیده
منابع مشابه
UNIQUENESS OF BEST PARAMETRIC INTERPOLATION BY CUBIC SPLINE CURVES by
Best parametric spline interpolation extends and refines the classical spline problem of best interpolation to (∗) inf t inf f { ∫ 1 0 ‖f (t)‖dt : f(ti) = yi, 1 ≤ i ≤ n} Here t : 0 = t1 < . . . < tn = 1 denotes a sequence of nodes and yi data in R d with y i 6= y i+1 . The R valued functionsf(t) lie componentwise in the Sobolev space L2(0, 1) and ‖ ‖ denotes the Euclidean norm in R. This proble...
متن کاملOn Free Knots
The aim of the present paper is to study free knots, a dramatic simplification of the notion of virtual knots also connected to finite type invariants, curves on surfaces and other objects of low-dimensional topology. It turns out that the objects of such sort (a factorization of arbitrary graphs modulo three formal Reidemeister moves) can be studied by using some very much simpler objects: in ...
متن کاملHierarchical Spline Approximations
1 Center for Image Processing and Integrated Computing (CIPIC), Department of Computer Science, University of California, Davis, CA 95616-8562, U.S.A.; e-mail: {wiley, hamann, joy}@cs.ucdavis.edu 2 University of Kaiserslautern, Fachbereich Informatik, P.O. Box 3049, D-67653 Kaiserslautern, Germany; e-mail: {bertram, scheuer}@informatik.uni-kl.de 3 Pixar Feature Division, Pixar Animation Studios...
متن کاملOn Spline Approximations for Bayesian Computations
Probabilistic reasoning su ers from NP-hard implementations. In particular, the amount of probabilistic information necessary to the computations is often overwhelming. For example, the size of conditional probability tables in Bayesian networks has long been a limiting factor in the general use of these networks. We present a new approach for manipulating the probabilistic information given. T...
متن کاملOn the shape control of B-spline curves by knots
B-spline curves and their rational generalizations (NURBS curves) play central role and are widely used in computer aided design today. A B-spline curve is uniquely defined by its degree, control points and knot values, while in terms of NURBS curves the weight vector has to be specified in addition. The modification of a curve is also an essential problem in CAD systems, hence numerous methods...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1974
ISSN: 0021-9045
DOI: 10.1016/0021-9045(74)90023-9