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On the conditioning of the Newton formula for Lagrange interpolation
Journal of Mathematical Analysis and Applications, 2022 The authors study the conditioning of the Newton formula for the interpolation polynomial. They expected that the Chebyshev points are the solutions of the problem, but the proofs are not available yet. They use the \(\mathfrak{R}\)-Leja points that give a good stability property for interpolation problems.
Phung Van Manh
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Inverse central ordering for the Newton interpolation formula
Numerical Algorithms, 2022 AbstractAn inverse central ordering of the nodes is proposed for the Newton interpolation formula. This ordering may improve the stability for certain distributions of nodes. For equidistant nodes, an upper bound of the conditioning is provided.
J M Carnicer, Y Khiar, J M Pena
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Central orderings for the Newton interpolation formula [PDF]
BIT Numerical Mathematics, 2019 The stability properties of the Newton interpolation formula depend on the order of the nodes and can be measured through a condition number. Increasing and Leja orderings have been previously considered (Carnicer et al. in J Approx Theory, 2017. https://doi.org/10.1016/j.jat.2017.07.005; Reichel in BIT 30:332–346, 1990).
J M Carnicer, Y Khiar, J M Pena
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A Newton type rational interpolation formula
Advances in Applied Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amy M Fu, Alain Lascoux
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Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula [PDF]
Journal of Mathematical Physics, 2010 We investigate the asymptotic behavior of the Selberg-like integral \documentclass[12pt]{minimal}\begin{document}$\frac{1}{N!}\int _{[0,1]^N}x_1^p$\break $\prod _{i<j}(x_i-x_j)^2\prod _ix_i^{a-1}(1-x_i)^{b-1}dx_i,$\end{document}1N!∫[0,1]Nx1p∏i<j(xi−xj)2∏ixia−1(1−xi)b−1dxi, as N → ∞ for different scalings of the parameters a and b with N ...
Jean-Gabriel Luque +2 more
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Newton–Simpson-based predictor–corrector methods for milling chatter stability prediction [PDF]
Scientific ReportsMilling chatter, a form of self-excited vibration, can cause significant damage in machining and manufacturing processes. By selecting appropriate milling parameters, milling chatter can be effectively mitigated without sacrificing milling efficiency ...
Yongjian Ji +5 more
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Intelligent trapezoid and variable weight combination-based reconstructed GM model [PDF]
HeliyonThe GM(1,1) model's prediction accuracy is significantly influenced by the accuracy of background value estimation. The traditional trapezoidal background value can only be applied to a specific data sequence.
Shanhua Zhang, Hong Ki An, Hongmei Yin
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Malaysia Journal of Invention and Innovationi-Dash is an innovative application designed to revolutionize the estimation of distance traveled by implementing sophisticated mathematical models such as the Newton Forward Divided Difference Interpolation Formula. By integrating this formula within
Zubaidah Sadikin +5 more
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Investigation of the Properties of a New Class of Interpolation Polynomials Based on Fibonacci Numbers [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, a class of new polynomials based on Fibonacci sequence using Newton interpolation is introduced. This target is performed once using Newton forward- divided- difference formula and another more using Newton backward- divided- difference ...
Moosa Ebadi, Sareh Haghkhah
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Mathematics, 2023 A nonlinear equation f(x)=0 is mathematically transformed to a coupled system of quasi-linear equations in the two-dimensional space. Then, a linearized approximation renders a fractional iterative scheme xn+1=xn−f(xn)/[a+bf(xn)], which requires one ...
Chein-Shan Liu +2 more
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