Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows
نویسندگان
چکیده
We analytically investigate univariate C continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows.
منابع مشابه
Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm
We compare univariateL1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than...
متن کاملPii: S0167-8396(02)00087-0
We investigate C1-smooth univariate curvature-based cubic L1 interpolating splines in Cartesian and polar coordinates. The coefficients of these splines are calculated by minimizing the L1 norm of curvature. We compare these curvature-based cubic L1 splines with second-derivative-based cubic L1 splines and with cubic L2 splines based on the L2 norm of curvature and of the second derivative. In ...
متن کاملGeometric dual formulation for first-derivative-based univariate cubic L 1 splines
With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C1-smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating t...
متن کاملShape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines
Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...
متن کاملFast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization
[Her13] F.Hernoux, R.Béarée, L.Gajny, E.Nyiri, J.Bancalin, O.Gibaru, Leap Motion pour la capture de mouvement 3D par spline L1. Application à la robotique. GTMG 2013, Marseille, 27-28 mars 2013 [Gib1899] J. Willard Gibbs, lettre à l’éditeur, Nature 59 (April 27, 1899) 606. [Lav00] J.E. Lavery, Univariate Cubic Lp splines and shape-preserving multiscale interpolation by univariate cubic L1 splin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Algorithms
دوره 3 شماره
صفحات -
تاریخ انتشار 2010