Results 191 to 200 of about 145,652 (224)
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
T. N. T. Goodman, S. L. Lee
openalex +3 more sources
A generalization of the variation diminishing property
Advances in Computational Mathematics, 1995 Several 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
J. M. Carnicer +2 more
openalex +3 more sources
A refinement of the variation diminishing property of Bézier curves
Computer Aided Geometric Design, 2009 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
openalex +3 more sources
On the Variation-Diminishing Property
Results in Mathematics, 1998 This 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.
Ioan Gavrea +2 more
openalex +3 more sources
Convexity and variation diminishing property of multidimensional Bernstein polynomials
Approximation Theory and its Applications, 1989 A necessary and sufficient condition for the convexity of the Bezier surface over the k-dimensional simplex is presented. We also consider a multidimensional version of the variation diminishing property of the Bernstein polynomials.
Marek Beśka
openalex +2 more sources
Variation diminishing property of densities of uniform generalized order statistics
Metrika, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Bieniek
openalex +3 more sources
Convexity and Variation Diminishing Property of Bernstein Polynomials over Triangles
, 1985 Let Bn(f;P) denote the Bernstein polynomials over triangle T and \({\hat f_n}\) denote the Bezier net associated with Bn(f;P). A certain type of variations of \({\hat f_n}\) is introduced by GOODMAN quite recently. In the present paper the corresponding variation of Bn(f;P) is defined by integration of the absolute value of the Laplacian of BP(f;P ...
Gengzhe Chang, Josef Hoschek
openalex +2 more sources
Is there a geometric variation diminishing property for B-spline or Bézier surfaces?
Computer Aided Geometric Design, 1992 The 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.
Hartmut Prautzsch, Tim Gallagher
openalex +2 more sources
Stepsize Restrictions for the Total-Variation-Diminishing Property in General Runge--Kutta Methods
SIAM Journal on Numerical Analysis, 2004 The numerical solution of the Cauchy problem for a partial differential equation of the type \[ {\partial \over \partial t} u(x,t) + {\partial \over \partial x} f(u(x,t)) =0, \quad t \geq 0\;\;-\infty < x < \infty \] is investigated. Using the method of lines the numerical problem leads to solving a system of ordinary differential equations of the form
Luca Ferracina, M. N. Spijker
openalex +2 more sources
Further variation diminishing properties of Bernstein polynomials on triangles
Constructive Approximation, 1987 The 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
openalex +2 more sources