Results 161 to 170 of about 3,918,663 (185)
A refinement of the variation diminishing property of Bézier curves
Computer Aided Geometric Design, 2010 For a given polynomial F(t)[email protected]?"i"="0^np"iB"i^n(t), expressed in the Bernstein basis over an interval [a,b], we prove that the number of real roots of F(t) in [a,b], counting multiplicities, does not exceed the sum of the number of real roots in [a,b] of the polynomial G(t)[email protected]?"i"="k^lp"iB"i"-"k^l^-^k(t) (counting ...
Rachid Ait-Haddou +2 more
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Interpolatory and variation-diminishing properties of generalized B-splines
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984 SynopsisWe consider classes of functions satisfying certain simple criteria of sign and smoothness and a decomposition property. It is known that these properties are possessed by Chebysheffian B-splines and it is shown here that they are also possessed by certain trigonometric B-splines. For such a class of functions, we derive a variation-diminishing
Goodman, T. N. T., Lee, S. L.
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On the Variation-Diminishing Property
Results in Mathematics, 1998This paper considers a new approach in proving the so-called strong variation-diminishing property for positive linear operators. Further it presents applications for the Durrmeyer operators with Jacobi weights \(t^\alpha (1-t)^\beta\), \(\alpha, \beta>-1\) and also for the family of operators \(P_n\) introduced by the reviewer (\textit{D. H.
Gavrea, Ioan +2 more
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Variation diminishing property of densities of uniform generalized order statistics
Metrika, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Bieniek
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Is there a geometric variation diminishing property for B-spline or Bézier surfaces?
Computer Aided Geometric Design, 1992The authors present a list of interesting examples which show that there is probably no simple geometric characterization of the variation diminishing property of B-spline or Bézier-surfaces -- in direct contrast to the case of the corresponding curves.
Prautzsch, Hartmut, Gallagher, Tim
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Further variation diminishing properties of Bernstein polynomials on triangles
Constructive Approximation, 1987The author gives a new definition of the `variation' of a surface which generalizes those considered previously. See \textit{G. Chang} and \textit{J. Hoschek}, Multivariate Approximation Theory III, Proc. Conf. Oberwolfach/Ger. 1985, ISNM 75, 61-70 (1985; Zbl 0563.41008). It is shown that the variation of a Bernstein polynomial on a triangle is bounded
T N T Goodman
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Stepsize Restrictions for the Total-Variation-Diminishing Property in General Runge--Kutta Methods
SIAM Journal on Numerical Analysis, 2004Much attention has been paid in the literature to total-variation-diminishing (TVD) numerical processes in the solution of nonlinear hyperbolic differential equations. For special Runge--Kutta methods, conditions on the stepsize were derived that are sufficient for the TVD property; see, e.g., Shu and Osher [J. Comput. Phys., 77 (1988), pp.
L. Ferracina, M. N. Spijker
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Variation diminishing properties and convexity for the tensor product Bernstein operator
Lecture Notes in Mathematics, 1992A. S. Cavaretta, A. Sharma
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Variation Diminishing Hankel Operators
, 2020 This paper studies the variation diminishing property of linear time-invariant Hankel k-positive systems, i.e., systems whose Hankel operator maps inputs with k - 1 sign changes to outputs with at most the same variation.
Rodolphe Sepulchre, Christian Grussler
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A generalization of the variation diminishing property
Advances in Computational Mathematics, 1995Several generalizations of the ordinary variation diminishing property are derived in the sense that, given an \(m \times n\) totally positive matrix \(T\) and an \(n \times r\) matrix \(A\) satisfying some additional conditions, then the number of changes of sign in the consecutive \(r \times r\) minors of \(TA\) is bounded by the number of changes of
Jesús M. Carnicer +2 more
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