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

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

...) methods based on non-polynomial approximation spaces for solving time dependent problems...

Discontinuous Galerkin method | Wronskian | Non-polynomial approximation space | Extended Tchebycheff system | Approximation rate | Errors | Approximation | Basis functions | Mathematical analysis | Polynomials | Criteria | Estimates | Galerkin methods

Discontinuous Galerkin method | Wronskian | Non-polynomial approximation space | Extended Tchebycheff system | Approximation rate | Errors | Approximation | Basis functions | Mathematical analysis | Polynomials | Criteria | Estimates | Galerkin methods

Journal Article

JOURNAL OF COMPUTATIONAL PHYSICS, ISSN 0021-9991, 09/2016, Volume 320, pp. 33 - 39

...) methods based on non-polynomial approximation spaces for solving time dependent problems...

Discontinuous Galerkin method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Wronskian | Non-polynomial approximation space | STABILITY | Extended Tchebycheff system | SYSTEMS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | Approximation rate

Discontinuous Galerkin method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Wronskian | Non-polynomial approximation space | STABILITY | Extended Tchebycheff system | SYSTEMS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FINITE-ELEMENT-METHOD | Approximation rate

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

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

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

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

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

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

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

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

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

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

A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a...

非线性方程组 | 正交多项式 | 系统 | 唯一性定理 | 高斯求积公式 | 应用 | 切比雪夫 | extended Chebyshev system | 33C45 | Gaussian Birkhoff quadrature formula | uniqueness theorems | Gaussian quadrature formula | Theoretical, Mathematical and Computational Physics | Mathematics | power orthogonal polynomials | Applications of Mathematics | Math Applications in Computer Science | 42C05 | MATHEMATICS, APPLIED | GAUSSIAN QUADRATURE-FORMULAS | Computer science | Forests and forestry | Gaussian processes

非线性方程组 | 正交多项式 | 系统 | 唯一性定理 | 高斯求积公式 | 应用 | 切比雪夫 | extended Chebyshev system | 33C45 | Gaussian Birkhoff quadrature formula | uniqueness theorems | Gaussian quadrature formula | Theoretical, Mathematical and Computational Physics | Mathematics | power orthogonal polynomials | Applications of Mathematics | Math Applications in Computer Science | 42C05 | MATHEMATICS, APPLIED | GAUSSIAN QUADRATURE-FORMULAS | Computer science | Forests and forestry | Gaussian processes

Journal Article

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