On the history of multivariate polynomial interpolation

DOI10.1016/S0377-0427(00)00353-8zbMath0968.65008OpenAlexW2135359007MaRDI QIDQ1590777

Thomas Sauer, Mariano Gasca

Publication date: 2 September 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00353-8

zbMATH Keywords

historymultivariate interpolationpolynomial interpolation

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) History of numerical analysis (65-03) History of approximations and expansions (41-03)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multivariate Hermite interpolation by algebraic polynomials: A survey
• Polynomial interpolation in several variables
• Piecewise Hermite interpolation in one and two variables with applications to partial differential equations
• On the finite element method
• Multipoint Taylor formulas and applications to the finite element method
• General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
• Divided differences for functions of two variables for irregularly spaces arguments
• Zur mechanischen Kubatur
• Note on Multivariate Interpolation for Unequally Spaced Arguments, with an Application to Double Summation
• Interpolation in Several Variables
• On a Class of Finite Elements Generated by Lagrange Interpolation
• On Multivariate Lagrange Interpolation
• The Remainder of Certain Linear Approximation Formulas in Two Variables
• DERIVATION OF INTERPOLATION FORMULAS IN SEVERAL INDEPENDENT VARIABLES*
• Approximation et interpolation des fonctions différentiables de plusieurs variables
• Some observations on interpolation in higher dimensions
• On a Class of Finite Elements Generated by Lagrange Interpolation. II
• Formulas for Bivariate Hyperosculatory Interpolation
• A Bivariate Generalization of Hermite's Interpolation Formula
• Tables of Coefficients for Interpolating in Functions of the Variables
• Remainders as Integrals of Partial Derivatives
• Note on interpolation for a function of several variables
• Remainders: functions of several variables

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