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Mathematical Analysis and Experimental Implementation of a Self-Calibration Method for Ultra-Precision Displacement Sensors. [PDF]
Sensors (Basel)Zhang Z, Liu X, Sato R, Gao W.
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A representation of the interpolation polynomial
Numerical Algorithms, 2021The authors give an interesting result about interpolation polynomial. Exactly, they obtain the generalized Hermite interpolant and several new identities on interpolation theory using a general recurrence interpolation formula and its applications. Some examples are given.
Mircea Ivan, Vicuta Neagos
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On polynomial interpolation of intervals
2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery, 2010Interpolation methods have been very popular in many practical problems. To estimate a function value y for a given x, we need to measure several pairs of (x i , y i ). In some problems, we do not know the exact value of the measured quantities, due to the inevitable measurement inaccuracy.
Yongchao Hou, Haiquan Qiu
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On Zeros of Interpolating Polynomials
SIAM Journal on Mathematical Analysis, 1986Polynomials to be used in interpolation of digital signals are called interpolating polynomials. They may require modification to assure convergence of their reciprocals on the unit circle. This paper concerns discrete time windowing, which consists of scaled truncation of a series such as \[ P_ N(z)\quad \triangleq \quad 1+\sum^{\infty}_{m=1}(z^ m+z^{-
Barnard, Roger W. +2 more
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Interpolation with symmetric polynomials
Numerical Algorithms, 2016Interpolation problems in more than one dimensional ambient spaces are studied in this article. Whenever the dimension of the ambient space is more than one, these problems are a lot more difficult to analyse than the classical univariate problems, for instance because not only convergence properties but also existence questions of interpolants ...
Jesús M. Carnicer, Carmen Godés
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Journal of Computational and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abderrahim Messaoudi +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abderrahim Messaoudi +2 more
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A Note on Polynomial Interpolation
International Journal of Computer Mathematics, 2002The Neville's algorithm and the Aitken's algorithm are successively linear interpolation approach to high degree Lagrangian interpolation. This note proposes a new approach with iteratively quadratic interpolation to high degree Lagrangian interpolation. The new algorithm here is cheaper (about 20% cheaper) than the Neville's algorithm.
Waléria Adriana Gonçalez Cecilio +5 more
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Polynomial Interpolation on the Unit Sphere
SIAM Journal on Numerical Analysis, 2003The main result of the paper provides families of points on the unit sphere in \(\mathbb R^3\), which admit unique solution to the problem of interpolation at these points by spherical polynomials of 3 variables of any given degree [cf. \textit{B. Bojanov} and \textit{Y. Xu}, SIAM J. Numer. Anal. 39, 1780--1793 (2002; Zbl 1014.41002)].
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On Geometric Interpolation by Polynomial Curves
SIAM Journal on Numerical Analysis, 2004Curve interpolation in several dimensions is studied. The curves are formed by parametric polynomials. Conditions for the existence of solutions are given which are necessary and sufficient. Moreover, uniqueness of the interpolating curve is also established.
Jernej Kozak, Emil Zagar
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