A New Approach to Newton-Type Polynomial Interpolation with Parameters
Joint Authors
Wang, Xiaofeng
Chen, Yanping
Zou, Le
Song, Liangtu
Weise, Thomas
Zhang, Chen
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-17
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zou, Le& Song, Liangtu& Wang, Xiaofeng& Weise, Thomas& Chen, Yanping& Zhang, Chen. 2020. A New Approach to Newton-Type Polynomial Interpolation with Parameters. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1201950
Modern Language Association (MLA)
Zou, Le…[et al.]. A New Approach to Newton-Type Polynomial Interpolation with Parameters. Mathematical Problems in Engineering No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1201950
American Medical Association (AMA)
Zou, Le& Song, Liangtu& Wang, Xiaofeng& Weise, Thomas& Chen, Yanping& Zhang, Chen. A New Approach to Newton-Type Polynomial Interpolation with Parameters. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1201950
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1201950