Topic
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.
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07 Jul 2015
TL;DR: Another way to determine the initial coefficients by using the polynomial representation on short intervals of the spline function and his derivatives is presented.
Abstract: The problem of interpolation a set of data is an old one, but the demanding of flexibility and high speed in operating on-line and in real time processing need to find new methods and improve the old ones [1]. The main properties of B-spline functions offer the possibility to implement algorithms of interpolation in a faster and optimal manner. A function can be represented by B-spline functions with a set of coefficients. For interpolative signal reconstruction it is necessary to calculate those coefficients. In this paper, for cubic spline interpolation it is analyzed a known algorithm and some of his deficiencies. Also there are relieved some possibilities for developing new algorithms that could eliminate those problems. It is presented another way to determine the initial coefficients by using the polynomial representation on short intervals of the spline function and his derivatives. Based on this results are made several observations for further use in improving the algorithm.
8 citations
TL;DR: In this article, the authors show how to represent the Hermite Martensen spline recursively and explicitly in terms of the B-spline by using the famous Marsden identity.
8 citations
01 Apr 1990
TL;DR: In this paper, it was shown that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial L n [f,x], generated by the nth row of the matrix, does not tend uniformly to f(x).
Abstract: From the well known theorem of G. Faber it follows that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial L n [f,x], generated by the nth row of the matrix, does not tend uniformly to f(x). We shall provide analogous results for the related operator H n,3 [f,x] as defined below
8 citations
TL;DR: Results show that, for a PC data acquisition system already equipped with a DSP board, the interpolator can render the need for a hardware reconstruction filter at the output of a digital-to-analogue converter (DAC) unnecessary.
8 citations
TL;DR: The differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper and show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and unequally spaced data.
Abstract: 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 unequally spaced data. The formulas based on cubic spline interpolation solving numerical integral of discrete function are deduced. The degree of integral formula is n=3.The formulas has high accuracy. At last, these calculation methods are illustrated through examples.
8 citations