Abstract— A smooth curve interpolation is very significant in computer graphics or in data visualization. In the present paper -piecewise rational cubic spline function with tension parameter is considered which produces a monotonic interplant to a given monotonic data set. The parameters in the description of the spline curve can be used to modify the shape of the curve, locally and globally. ...

In this paper, we introduce a new d-Spline based Incremental Performance Parameter Estimation method (IPPE ). We first define a fitting function d-Spline, which has high flexibility to adapt given data and can be easily computed. The complexity of d-Spline is O(n). We introduce a procedure for incremental performance parameter estimation and an example of data fitting using d-Spline. We applied...

Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and u...

Given a finite subset Ξ ⊂ R and data |Ξ , the surface spline interpolant to the data |Ξ is a function s which minimizes a certain seminorm subject to the interpolation conditions |Ξ = |Ξ . It is known that surface spline interpolation is stable on the Sobolev space W in the sense that ‖s‖L∞(Ω) ≤ const ‖f‖Wm , where m is an integer parameter which specifies the surface spline. In this note we sh...

In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose-response relationship and to find the smallest target dose concentration d(*), which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose-respo...

The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B...

In this paper, boundary value problems of fractional order are converted into an optimal control problems. Then an approximate solution is constructed from translations and dilations of a B-spline function such that the exact boundary conditions are satisfied. The fractional differential operators are taken in the Riemann-Liouville and Caputo sense. Several example are given and the optimal err...

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...