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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2019, Volume 349, pp. 265 - 278
.... We show that the structure of extended Tchebycheff spaces allows us to fully generalize the dimension upper bounds known in the literature for polynomial spline spaces over T-meshes... 
Extended Tchebycheff spaces | Tchebycheffian spline spaces | Dimension instabilities | T-meshes | Dimension bounds | Dimension formula | POLYNOMIAL SPLINES | MATHEMATICS, APPLIED | Computer science
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 320, pp. 33 - 39
Journal Article
by Yang, H and Yoon, J
JOURNAL OF COMPUTATIONAL PHYSICS, ISSN 0021-9991, 09/2016, Volume 320, pp. 33 - 39
Journal Article
The Annals of Statistics, ISSN 0090-5364, 12/1983, Volume 11, Issue 4, pp. 1257 - 1262
.... For the polynomial regression model, a characterization of the space of consistent directions S was obtained in terms of the convergence rates of the corresponding design sequence to its limit points... 
Short Communications | Mathematical theorems | Least squares | Mathematical independent variables | Polynomials | Mathematical vectors | Regression analysis | Linear models | Consistent estimators | Estimators | 62J05 | least squares estimators | 62E20 | Asymptotic consistency | extended Tchebycheff system | consistency region | consistent direction | polynomial regression
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 217, Issue 2, pp. 790 - 800
Let U n ⊂ C n [ a, b] be an extended Chebyshev space of dimension n + 1. Suppose that f 0 ∈ U n is strictly positive and f 1... 
Bernstein operator | Exponential polynomial | Extended Chebyshev system | Bernstein polynomial | POLYNOMIALS | MATHEMATICS, APPLIED | BASES | SPACES | CURVES | Operators | Computation | Searching | Mathematical analysis | Images | Chebyshev approximation | Mathematical models | Mathematics - Classical Analysis and ODEs
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 2010, Volume 162, Issue 7, pp. 1407 - 1416
We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on... 
Bernstein operator | Extended Chebyshev space | Exponential polynomial | Bernstein polynomial | MATHEMATICS
Journal Article
Constructive Approximation, ISSN 0176-4276, 6/2009, Volume 29, Issue 3, pp. 345 - 367
...=0,…,n, of the space U n with the property that each p n,k has a zero of order k at a and a zero of order n... 
Bernstein operator | 41A35 | Analysis | Numerical Analysis | Extended Chebyshev system | Mathematics | 41A50 | Exponential polynomial | Bernstein polynomial | MATHEMATICS | BASES | SPACES | CONSTRUCTION | OPTIMAL STABILITY | Mathematics - Classical Analysis and ODEs
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 2004, Volume 131, Issue 1, pp. 47 - 58
A classical formula gives the blossom of the derivative of a polynomial function in terms of its own blossom. We extend this result to the Chebyshevian... 
Extended Chebyshev spaces | Chebyshev blossoms | Blossoms | MATHEMATICS | blossoms | extended Chebyshev spaces
Journal Article
Constructive Approximation, ISSN 0176-4276, 6/2014, Volume 39, Issue 3, pp. 573 - 583
The cycloidal spaces C n , generated by the trigonometric polynomials of degree 1 and algebraic polynomials of degree n... 
Extended Chebyshev spaces | Critical length | Mathematics | 41A50 | Cycloidal spaces | Numerical Analysis | Analysis | 42A10 | 41A10 | 65D17 | Shape preserving representations | 41A05 | Total positivity | Extended Chebyshev spaces | MATHEMATICS | CURVES
Journal Article
Calcolo, ISSN 0008-0624, 12/2019, Volume 56, Issue 4, pp. 1 - 12
Recently, Carnicer et al. (Calcolo 54(4):1521–1531, 2017) proved the very elegant and surprising fact that half of the critical length of a cycloidal space coincides with the first positive zero of a spherical Bessel function... 
Mathematics | Theory of Computation | Cycloidal spaces | Bessel functions | Extended Chebyshev spaces | Critical lengths | Numerical Analysis | 41A10 | 65D05 | 65D17 | 41A05 | 65D18 | 41A29
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 12/2012, Volume 52, Issue 4, pp. 1009 - 1034
The splines we investigate are piecewise Chebyshevian splines, in the sense of splines with pieces taken from different Extended Chebyshev spaces, and they satisfy parametric continuity conditions at the knots... 
Geometric design | Computational Mathematics and Numerical Analysis | Numeric Computing | Mathematics | Extended Chebyshev spaces | Generalised derivatives | Blossoms | Bernstein bases | Weight functions | Mathematics, general | 65D17 | B-spline bases | Total positivity | 65D07 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | BASES | CHEBYSHEV SPACES | Numerical Analysis
Journal Article
Numerical Algorithms, ISSN 1017-1398, 8/2005, Volume 39, Issue 4, pp. 399 - 414
The paper addresses the problem of how to ensure existence of blossoms in the context of piecewise spaces built from joining different extended Chebyshev spaces by means of connection matrices... 
geometric design | Hermite interpolation | Numeric Computing | blossoming | Theory of Computation | connection matrices | Algebra | Algorithms | Bernstein bases | Computer Science | piecewise extended Chebyshev spaces | Mathematics, general | B-spline bases | Geometric design | Blossoming | Connection matrices | Piecewise extended Chebyshev spaces | MATHEMATICS, APPLIED | SPACES | CURVES | BLOSSOMS
Journal Article
应用数学学报:英文版, ISSN 0168-9673, 2015, Volume 31, Issue 1, pp. 111 - 120
Journal Article
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