scholarly journals Algebraic Theory of Appell Polynomials with Application to General Linear Interpolation Problem

10.5772/46482 ◽  
2012 ◽  
Author(s):  
Francesco Aldo ◽  
Elisabetta Longo
Keyword(s):  
Interpolation Problem ◽  
Algebraic Theory ◽  
Linear Interpolation ◽  
General Linear ◽  
Appell Polynomials

scholarly journals Umbral interpolation

2016 ◽  
Vol 99 (113) ◽  
pp. 165-175 ◽  
Author(s):  
Francesco Costabile ◽  
Elisabetta Longo
Keyword(s):  
Interpolation Problem ◽  
Truncation Error ◽  
Linear Interpolation ◽  
General Linear ◽  
Numerical Examples ◽  
Sheffer Polynomials

A general linear interpolation problem is posed and solved. This problem is called umbral interpolation problem because its solution can be expressed by a basis of Sheffer polynomials. The truncation error and its bounds are considered. Some examples are discussed, in particular generalizations of Abel-Gontscharoff and central interpolation are studied. Numerical examples are given too.

scholarly journals An algebraic exposition of umbral calculus with application to general linear interpolation problem: A survey

2014 ◽  
Vol 96 (110) ◽  
pp. 67-83 ◽  
Author(s):  
Francesco Costabile ◽  
Elisabetta Longo
Keyword(s):  
Interpolation Problem ◽  
Linear Interpolation ◽  
Umbral Calculus ◽  
General Linear ◽  
Numerical Examples ◽  
Polynomial Sequences ◽  
Sheffer Sequences ◽  
Determinantal Form ◽  
Systematic Exposition ◽  
Sheffer Polynomial

A systematic exposition of Sheffer polynomial sequences via determinantal form is given. A general linear interpolation problem related to Sheffer sequences is considered. It generalizes many known cases of linear interpolation. Numerical examples and conclusions close the paper.

Research on Contour Interpolation in Reverse Engineering

2012 ◽  
Vol 170-173 ◽  
pp. 3304-3307
Author(s):  
Hong Liang Wang ◽  
Hai Fei Ding ◽  
Jin Qi Wang
Keyword(s):  
Rapid Prototyping ◽  
Reverse Engineering ◽  
Interpolation Problem ◽  
Minimum Distance ◽  
Linear Interpolation ◽  
Contour Interpolation ◽  
Vehicle Engine

In reverse engineering and rapid prototyping, several intermediate contours interpolated between adjacent two-layer ICT slice are needed to meet the requirement of rapid prototyping. A method of linear interpolation based on minimum distance is adopted in this paper. On the basis of the research on interpolation problem between single contours, some researches on the interpolation problem of multiply contours was done in this paper. Satisfactory results are attained by the experiments of a vehicle engine.

scholarly journals On a linear interpolation problem for n-dimensional vector polynomials

2015 ◽  
Vol 199 ◽  
pp. 45-62 ◽  
Author(s):  
Mikhail Kudryavtsev ◽  
Sergio Palafox ◽  
Luis O. Silva
Keyword(s):  
Interpolation Problem ◽  
Linear Interpolation ◽  
Dimensional Vector

scholarly journals General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 964
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Differential Equations ◽  
Linear Functional ◽  
Recurrence Relations ◽  
Linear Interpolation ◽  
Appell Polynomials ◽  
Polynomial Sequences ◽  
Matrix Calculus

An approach to general bivariate Appell polynomials based on matrix calculus is proposed. Known and new basic results are given, such as recurrence relations, determinant forms, differential equations and other properties. Some applications to linear functional and linear interpolation are sketched. New and known examples of bivariate Appell polynomial sequences are given.

EEG-fMRI: Including sleep-induced potentials in the general linear model improves spatial accordance with epileptic focus

2010 ◽  
Vol 41 (02) ◽  
Author(s):  
J Möhring ◽  
D Coropceanu ◽  
F Möller ◽  
S Wolff ◽  
R Boor ◽  
...  
Keyword(s):  
Linear Model ◽  
General Linear Model ◽  
General Linear ◽  
Epileptic Focus
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