ECT-B-splines defined by generalized divided differences

2006 ◽  
Vol 187 (1) ◽  
pp. 96-122 ◽  
Author(s):  
G. Mühlbach
Keyword(s):  
Divided Differences ◽  
B Splines

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 Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

2021 ◽  
Vol 381 ◽  
pp. 113779
Author(s):  
Wenbin Hou ◽  
Kai Jiang ◽  
Xuefeng Zhu ◽  
Yuanxing Shen ◽  
Ping Hu
Keyword(s):  
Isogeometric Analysis ◽  
B Splines ◽  
Discontinuous Problems

scholarly journals Interpolation and Sampling with Exponential Splines of Real Order

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Massopust
Keyword(s):  
Positive Real ◽  
B Splines

AbstractThe existence of fundamental cardinal exponential B-splines of positive real order $$\sigma $$ σ is established subject to two conditions on $$\sigma $$ σ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented.

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