Use of Divided Differences and B Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids

2005 ◽  
Vol 77 (5-6) ◽  
pp. 686-694 ◽  
Author(s):  
I. V. Oseledets
Keyword(s):  
Divided Differences ◽  
Nonuniform Grids ◽  
B Splines ◽  
Discrete Transforms

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.

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

scholarly journals On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 310 ◽  
Author(s):  
Pedro Ortiz ◽  
Juan Carlos Trillo
Keyword(s):  
Initial Data ◽  
Numerical Experiments ◽  
Approximation Order ◽  
Piecewise Polynomial ◽  
Nonuniform Grids ◽  
Uniform Grids ◽  
Reconstruction Operator ◽  
Convexity Properties ◽  
Second Degree

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

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