On a Generalization of Cubic Spline Interpolation

نویسندگان

  • Shang Gao
  • Zaiyue Zhang
  • Cungen Cao
چکیده

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arbitrary two nodes or second derivatives of arbitrary two node are given. At last, these calculation methods are illustrated through examples.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Piecewise cubic interpolation of fuzzy data based on B-spline basis functions

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

متن کامل

A Continuous Self-Organizing Map using Spline Technique for Function Approximation

We propose a new method called C-SOM for function approximation. C-SOM extends the standard Self-Organizing Map (SOM) with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve standard SOMs' generalization capabilities. CSOM uses the gradient information provided by the LLM technique to compute a cubic spline interpolation in the input space bet...

متن کامل

DC-Splines: Revisiting the Trilinear Interpolation on the Body-Centered Cubic Lattice

In this paper, we thoroughly study a trilinear interpolation scheme previously proposed for the Body-Centered Cubic (BCC) lattice. We think that, up to now, this technique has not received the attention that it deserves. By a frequency-domain analysis we show that it can isotropically suppress those aliasing spectra that contribute most to the postaliasing effect. Furthermore, we present an eff...

متن کامل

Piecewise Polynomial Kernels for Image Interpolation: A Generalization of Cubic Convolution

A well-known approach to image interpolation is cubic convolution, in which the ideal sinc function is modelled by a finite extent kernel, which consists of piecewise third order polynomials. In this paper we show that the concept of cubic convolution can be generalized. We derive kernels of up to ninth order and compare them both mutually and to cardinal splines of corresponding orders. From s...

متن کامل

ON INTERPOLATION of FUNCTIONS with a BOUNDARY LAYER BY CUBIC SPLINES

The problem of article is cubic spline-interpolation of functions having high gradient regions. It is shown that uniform grids are inefficient to be used. In case of piecewise-uniform grids, concentrated in the boundary layer, for cubic spline interpolation are announced asymptotically exact estimates on a class of functions with an exponential boundary layer. There are obtained results showing...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • JSW

دوره 6  شماره 

صفحات  -

تاریخ انتشار 2011