Monotone cubic interpolation

About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.

The study of cubic uniform rational B-spline interpolation algorithm

Abstract: Interpolation algorithm is a fundamental one in the robot system.In this paper a cubic Uniform Rational B-Spline interpolation algorithm is studied.Basing on cubic Non-Uniform Rational B-Spline(NURBS),the expression of cubic Uniform Rational B-Spline has gotten.The law of B-spline control points in the cubic Uniform Rational B-Spline is discovered,which will make calculation simple.What's more,the algorithm is very practical by considering the problem of acceleration-deceleration control.Finally,use cubic Uniform Rational B-spline interpolation to fit the helical line.The algorithm has been tested in simulation yielding good results.

Cubic spline functions and polynomials for calculation of absorption rate.

Abstract: A model-independent method for calculation of the absorption rate based on an exact mathematical solution to the deconvolution problem of systems with linear pharmacokinetics and a polyexponential impulse responses has been examined. Theoretical analysis shows how a noninteracting primary input can be precisely evaluated when data on blood levels from a known source such as an i.v. bolus or zero-order infusion are available. This work compares the use of a Lagrange 3rd degree polynomial with that of a cubic spline function (special 3rd degree polynomial) for calculation of the absorption rate. The method is compared to another using simulated data (12 data points) containing various degrees of random noise. The accuracy of the methods is determined by how well the estimates represent the true values. It was found that the accuracy of the two methods was not significantly different, and that it was of the same order of magnitude as the noise level of the data.

Efficient algorithms for periodic Hermite spline interpolation

Abstract: Periodic Hermite spline interpolants on an equidistant lattice are represented by the Bézier technique as well as by the fi-spline method. Circulant matrices are used to derive new explicit formulas for the periodic Hermite splines of degree m and defect r (1 < r < m). Applying the known de Casteljau algorithm and the de Boor algorithm, respectively, we obtain new efficient real algorithms for periodic Hermite spline interpolation. 0. INTRODUCTION This paper deals with periodic Hermite spline interpolation on the equidistant lattice Z. Other approaches to this problem use Euler-Frobenius polynomials and complex line integrals (see [4-6]) or Euler-Frobenius polynomials and circulant matrices (see [7, 8]). Similar to [7, 8], we prefer a real-algebraic method for periodic Hermite spline interpolation. Contrary to [4-8], we apply a vectorial Bézier technique and later a periodic 5-spline method in this note. This leads to new efficient real algorithms for periodic Hermite spline interpolation. These methods are based on the de Casteljau algorithm and the de Boor algorithm, respectively. Both procedures possess a low arithmetic complexity. Further, one can see that the generalized Euler-Frobenius polynomials are very important for periodic Hermite spline interpolation. Note that our methods can be extended to periodic Hermite spline interpolation with shifted nodes too. 1. Preliminaries In this paper we use standard notations. First we recall some facts concerning circulant matrices, which form the background of the considerations in §§3 and 4 (cf. [2]). Let N £ N (N > 1) be fixed. For a = (ax, ... , aN)T £ RN , let ax a2 ■ ■ ■ un ' aw ax ■■■ üM-i

Interpolation in Algebraic Geometry

Abstract: This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. More recently, it was shown that one can always find nonspecial curves through the expected number of general points and linear spaces. After some expository material regarding scrolls, we consider the generalization of this question to varieties of all dimensions and explain why smooth varieties of minimal degree satisfy interpolation. We give twenty-two equivalent formulations of interpolation. We also classify when Castelnuovo curves satisfy weak interpolation. In the appendix, we prove that del Pezzo surfaces satisfy weak interpolation. Our techniques for proving interpolation include deformation theory, degeneration and specialization, and association.