Bernstein-type operators in Chebyshev spaces

DOI10.1007/s11075-008-9260-1zbMath1200.41023OpenAlexW2075238614MaRDI QIDQ841158

Marie-Laurence Mazure

Publication date: 14 September 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9260-1

zbMATH Keywords

Bernstein-type operatorstotal positivityshape preservationBernstein-type basesextended Chebychev spaces

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (18)

Greville abscissae of totally positive bases ⋮ Approximation by Chebyshevian Bernstein operators versus convergence of dimension elevation ⋮ Design with quasi extended Chebyshev piecewise spaces ⋮ Approximation by Müntz spaces on positive intervals ⋮ Geometrically continuous piecewise Chebyshevian NU(R)BS ⋮ Finding all systems of weight functions associated with a given extended Chebyshev space ⋮ The fundamental blossoming inequality in Chebyshev spaces. I: Applications to Schur functions ⋮ Extended Chebyshev spaces in rationality ⋮ The Hyers-Ulam stability constant for Chebyshevian Bernstein operators ⋮ Quadratic convergence of approximations by CCC-Schoenberg operators ⋮ Voronovskaja-type theorem for modified Bernstein operators ⋮ Generalized Bernstein operators on the classical polynomial spaces ⋮ Quasi extended Chebyshev spaces and weight functions ⋮ Dimension elevation is not always corner-cutting ⋮ Optimality of generalized Bernstein operators ⋮ Chebyshev--Schoenberg operators ⋮ Nested sequences of rational spaces: Bernstein approximation, dimension elevation, and Pólya-type theorems on positive polynomials ⋮ Critical length: an alternative approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The geometry of Tchebycheffian splines
• Chebyshev spaces and Bernstein bases
• On Chebyshevian spline subdivision
• Extended Chebyshev piecewise spaces characterised via weight functions
• Blossoms are polar forms
• On dimension elevation in quasi extended Chebyshev spaces
• Which spaces for design?
• Bernstein operators for exponential polynomials
• Blossoming: A geometrical approach
• Chebyshev spaces with polynomial blossoms
• Blossoms and optimal bases
• Chebyshev-Bernstein bases
• Critical length for design purposes and extended Chebyshev spaces
• Some results for a class of generalized polynomials
• Curve and surface construction using variable degree polynomial splines
• On a class of weak Tchebycheff systems
• Shape Constraints and Optimal Bases for $C^1$ Hermite Interpolatory Subdivision Schemes
• Ready-to-Blossom Bases in Chebyshev Spaces

This page was built for publication: Bernstein-type operators in Chebyshev spaces