consapp_newton.bib

@Inbook{Rutishauser1990,
author={{Rutishauser, H.}},
editor={{Gutknecht, M.}},
title="Interpolation",
bookTitle="Lectures on Numerical Mathematics",
year="1990",
publisher="Birkhäuser Boston",
address="Boston, MA",
pages="128--174",
abstract="Interpolation is the art of reading between the lines of a mathematical table. It can be used to express nonelementary functions approximately in terms of the four basic arithmetic operations, thus making them accessible to computer evaluation.",
isbn="978-1-4612-3468-5",
doi="10.1007/978-1-4612-3468-5_6",
url="https://doi.org/10.1007/978-1-4612-3468-5_6"
}
@Inbook{Scherer2010,
author={{Scherer, P. O.J.}},
title="Interpolation",
bookTitle="Computational Physics: Simulation of Classical and Quantum Systems",
year="2010",
publisher="Springer",
address="Berlin, Heidelberg",
pages="15--27",
abstract="Experiments usually produce a discrete set of data points. If additional data points are needed, for instance, to draw a continuous curve or to change the sampling frequency of audio or video signals, interpolation methods are necessary. But interpolation is also helpful to develop more sophisticated numerical methods for the calculation of numerical derivatives or integrals. Polynomial interpolation is discussed in large detail together with its drawbacks. The methods by Lagrange and Newton are discussed, as well as the Neville method, which allow efficient determination and evaluation of the interpolating polynomial. For interpolation over a larger range, larger number of data spline interpolation is very useful which does not show the oscillatory behavior characteristic of polynomial interpolation. In a computer experiment both these approaches are compared. Multivariate interpolation is a necessary tool to process multidimensional data sets, for instance, for image processing. A computer experiment compares bilinear interpolation and bicubic spline interpolation.",
isbn="978-3-642-13990-1",
doi="10.1007/978-3-642-13990-1_2",
url="https://doi.org/10.1007/978-3-642-13990-1_2"
}
@article{https://doi.org/10.1155/2020/9020541,
author = {{Zou, L., Song, L., Wang, X., Weise, T., Chen, Y., & Zhang, C.}},
title = {A New Approach to Newton-Type Polynomial Interpolation with Parameters},
journal = {Mathematical Problems in Engineering},
volume = {2020},
number = {1},
pages = {9020541},
doi = {10.1155/2020/9020541},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1155/2020/9020541},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1155/2020/9020541},
abstract = {Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.},
year = {2020}
}
@inbook{doi:10.1002/9781119604570.ch4,
author={{Epperson, J. F.}},
publisher = {John Wiley & Sons, Ltd},
isbn = {9781119604570},
title = {Interpolation and Approximation},
booktitle = {An Introduction to Numerical Methods and Analysis},
chapter = {4},
pages = {101-148},
doi = {10.1002/9781119604570.ch4},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119604570.ch4},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119604570.ch4},
year = {2021},
keywords = {divided differences, Hermite interpolation, interpolation error, inverse quadratic interpolation, Lagrange interpolation, Muller's method, Newton interpolation, piecewise polynomial interpolation, tension Splines},
abstract = {Summary This chapter presents the information of interpolation and approximation for solving problems of mathematical analysis. It contains exercises and solutions that present an introduction to key concepts, a calculus review, and an updated primer on Lagrange interpolation, Newton interpolation and divided differences, interpolation error, Muller's method and inverse quadratic interpolation, Hermite interpolation, piecewise polynomial interpolation, Splines, tension Splines, and least squares concepts in approximation. The chapter features new and updated material reflecting new trends and applications in numerical methods and analysis. It is the perfect for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.}
}
@article{tsao1977,
author={{Tsao, N.-K.}},
year={1977},
title={Newton interpolation is efficient for approximation of linear functionals},
journal={Numerische Mathematik},
page={115--122},
volume={29},
number={1},
abstract={The Newton interpolation approach is developed for approximation of linear functionals. It is shown that in numerical interpolation and numerical differentiation, the Newton interpolation approach is more efficient than solving the Vandermonde systems.},
doi={10.1007/BF01389317}
}