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Variation diminishing property

Known as: Variation diminishing properties, Variation diminishing property of Bézier curves, Variation diminishing property of totally positive matrices 
In mathematics, the variation diminishing property of certain mathematical objects involves diminishing the number of changes in sign (positive to… Expand
Wikipedia

Related topics

Related topics

6 relations
Bézier curveDescartes' rule of signsJacobi operatorLinear interpolation
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Broader (1)

Interpolation

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2020
2020
Dynamical Systems With a Cyclic Sign Variation Diminishing Property
In 1970, Binyamin Schwarz defined and analyzed totally positive differential systems (TPDSs), i.e., linear time-varying systems… Expand
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2019
2019
Direct transcription of optimal control problems with finite elements on Bernstein basis
The paper introduces the use of Bernstein polynomials as a basis for the direct transcription of optimal control problems with… Expand
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2017
2017
Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements
Abstract This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element… Expand
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2010
2010
A refinement of the variation diminishing property of Bézier curves
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… Expand
2008
2008
Nonlinear subdivision through nonlinear averaging
We investigate a general class of nonlinear subdivision algorithms for functions of a real or complex variable built from linear… Expand
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Highly Cited
2004
Highly Cited
2004
Stepsize Restrictions for the Total-Variation-Diminishing Property in General Runge-Kutta Methods
Much attention has been paid in the literature to total-variation-diminishing (TVD) numerical processes in the solution of… Expand
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1996
1996
On zero curves of bivariate polynomials
  • M. Floater
  • Adv. Comput. Math.
  • 1996
    • Corpus ID: 15964638
Two conditions on the signs of the coefficients of a bivariate polynomial which ensure that the zero set is a single curve are… Expand
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1992
1992
Is there a geometric variation diminishing property for B-spline or Bézier surfaces?
Abstract We present examples which show that simple geometric concepts of a variation diminishing property do not work for tensor… Expand
1989
1989
Convexity and variation diminishing property of multidimensional Bernstein polynomials
A necessary and sufficient condition for the convexity of the Bézier surface over the k-dimensional simplex is presented. We also… Expand
1985
1985
Markov chains and computer aided geometric design: Part II—examples and subdivision matrices
In Part I, Markov chains were shown to be associated with solutions to several standard problems in computer-aided geometric… Expand
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