Hermite interpolation and its numerical differentiation formula involving symmetric functions

2009 ◽  
Vol 24 (3) ◽  
pp. 309-314 ◽  
Author(s):  
Hong-huan Bai ◽  
Ai-min Xu
Keyword(s):  
Symmetric Functions ◽  
Hermite Interpolation ◽  
Numerical Differentiation ◽  
Differentiation Formula ◽  
Numerical Differentiation Formula

scholarly journals Numerical differentiation on scattered data through multivariate polynomial interpolation

2021 ◽  
Author(s):  
Francesco Dell’Accio ◽  
Filomena Di Tommaso ◽  
Najoua Siar ◽  
Marco Vianello
Keyword(s):  
Polynomial Interpolation ◽  
Numerical Differentiation ◽  
Scattered Data ◽  
Monomial Basis ◽  
Multivariate Polynomial Interpolation ◽  
Differentiation Formula ◽  
Local Polynomial ◽  
Leja Points ◽  
Derivatives Of ◽  
Numerical Differentiation Formula

AbstractWe discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.

CLASSES OF WEIGHTED SYMMETRIC FUNCTIONS

1988 ◽  
Vol 14 (2) ◽  
pp. 429
Author(s):  
Tran
Keyword(s):  
Symmetric Functions

WEIGHTED SYMMETRIC FUNCTIONS

1989 ◽  
Vol 15 (1) ◽  
pp. 313
Author(s):  
Tran
Keyword(s):  
Symmetric Functions
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