scholarly journals Weighted means of B-splines, positivity of divided differences, and complete homogeneous symmetric polynomials

2021 ◽  
Vol 608 ◽  
pp. 68-83 ◽  
Author(s):  
Albrecht Böttcher ◽  
Stephan Ramon Garcia ◽  
Mohamed Omar ◽  
Christopher O'Neill
Keyword(s):  
Divided Differences ◽  
Symmetric Polynomials ◽  
B Splines ◽  
Weighted Means

SOME REMARKS ABOUT THE CONNECTION BETWEEN FRACTIONAL DIVIDED DIFFERENCES, FRACTIONAL B-SPLINES, AND THE HERMITE–GENOCCHI FORMULA

2008 ◽  
Vol 06 (02) ◽  
pp. 279-290 ◽  
Author(s):  
PETER MASSOPUST ◽  
BRIGITTE FORSTER
Keyword(s):  
Natural Extension ◽  
Divided Differences ◽  
Short Paper ◽  
Difference Operators ◽  
Fractional Difference ◽  
B Splines ◽  
Definition Of

Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators, and present a generalized Hermite–Genocchi formula. This formula then allows the definition of a larger class of fractional B-splines.

scholarly journals A note on divided differences

2015 ◽  
Vol 98 (112) ◽  
pp. 147-151 ◽  
Author(s):  
Ioan Gavrea ◽  
Mircea Ivan
Keyword(s):  
Recurrence Formula ◽  
Divided Differences ◽  
Symmetric Polynomials ◽  
Power Sums ◽  
Elementary Symmetric Polynomials

We obtain a new recurrence formula for sequences of divided differences. In a particular case, the recurrence formula simplifies the classical Newton-Girard identities relating power sums and elementary symmetric polynomials.

scholarly journals Divided differences and ideals generated by symmetric polynomials

1994 ◽  
Vol 126 (1-3) ◽  
pp. 209-215 ◽  
Author(s):  
A. Lascoux ◽  
P. Pragacz
Keyword(s):  
Divided Differences ◽  
Symmetric Polynomials

scholarly journals Milne’s volume function and vector symmetric polynomials

2009 ◽  
Vol 44 (5) ◽  
pp. 583-590 ◽  
Author(s):  
Emmanuel Briand ◽  
Mercedes Rosas
Keyword(s):  
Symmetric Polynomials ◽  
Volume Function

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines
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