Fitting a Cm - Smooth Function to Data
نویسنده
چکیده
Suppose we are given a finite subset E ⊂ R and a function f : E → R. How to extend f to a C function F : R → R with C norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function F , and for computing the order of magnitude of its C norm. The running time of our algorithms is never more than CN logN , where N is the cardinality of E and C is a constant depending only on m and n. ∗This work was partially supported by NSF grant #DMS-0245242 †Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590 §
منابع مشابه
Estimation of Hydrodynamic Forces on the Cylinderical Smooth Piles to Random Waves and Currents
Most Codes such as API and BSI recommend Morison’s equation to estimate hydrodynamic forces on offshore structures. Significant differences exist among these Codes due to using different methods of analysis and estimation of force coefficients. In this paper, data from full scale tests have been used to evaluate random waves and uniform current actions on the smooth piles.
 Four time an...
متن کاملEstimation of Hydrodynamic Forces on the Cylinderical Smooth Piles to Random Waves and Currents
Most Codes such as API and BSI recommend Morison’s equation to estimate hydrodynamic forces on offshore structures. Significant differences exist among these Codes due to using different methods of analysis and estimation of force coefficients. In this paper, data from full scale tests have been used to evaluate random waves and uniform current actions on the smooth piles. Four time and ...
متن کاملRegression Modeling for Spherical Data via Non-parametric and Least Square Methods
Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the areas that are most likely to constitute the presence of the animals. From a geome...
متن کاملInterpolation and Scattered Data Fitting on Manifolds using Projected Powell-Sabin Splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold Ω. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(Uξ , φξ)}ξ∈Ω satisfying certain conditions of smooth dependence on ξ. If Ω is a C2-manifold embedded into R3, then projections into tangent planes can be employed....
متن کاملSignal detection Using Rational Function Curve Fitting
In this manuscript, we proposed a new scheme in communication signal detection which is respect to the curve shape of received signal and based on the extraction of curve fitting (CF) features. This feature extraction technique is proposed for signal data classification in receiver. The proposed scheme is based on curve fitting and approximation of rational fraction coefficients. For each symbo...
متن کامل