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A geometric proof for the variation diminishing property of B-spline approximation [PDF]
Journal of Approximation Theory, 1983 AbstractA geometric proof for the variation diminishing property of B-spline approximation is given. The proof is based primarily upon a generalized form of the de Boor-Cox algorithm and the intuitively obvious fact that piecewise linear interpolation is variation diminishing. Previous proofs [4, 8] employed the mathematical methods of total positivity,
Richard Riesenfeld
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Global smoothness preservation and the variation-diminishing property
Journal of Inequalities and Applications, 1999 In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators.
Gavrea Ioan +4 more
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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, Taishin Nomura
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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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Variation diminishing-type properties for multivariate sampling Kantorovich operators [PDF]
Bolletino Dell Unione Matematica Italiana, 2020 AbstractIn this paper we establish a variation-diminishing type estimate for the multivariate Kantorovich sampling operators with respect to the concept of multidimensional variation introduced by Tonelli. A sharper estimate can be achieved when step functions with compact support (digital images) are considered.
Danilo Costarelli +2 more
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Dynamical Systems With a Cyclic Sign Variation Diminishing Property [PDF]
IEEE Transactions on Automatic Control, 2020 Several studies analyzed certain nonlinear dynamical systems by showing that the cyclic number of sign variations in the vector of derivatives is an integer-valued Lyapunov function. These results are based on direct analysis of the dynamical equation satisfied by the vector of derivatives, i.e. the variational system.
Guy Sharon +2 more
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Variation Diminishing Properties of Bernstein Polynomials on a Tetrahedron [PDF]
Journal of Approximation Theory, 1994 The authors extend to \(\mathbb{R}^ d\) various definitions of the notions of total variation of a function \(f\) defined on a simplex. The original definitions were given by \textit{T. N. T. Goodman} for functions defined on a triangle [see J. Approximation Theory 50, 111-126 (1987; Zbl 0618.41007) and Constructive Approximation 3, 297-305 (1987; Zbl ...
Bhatt, A., Ojha, A.
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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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Applied Sciences, 2022 A key technique for modeling 2D objects is built using a Bézier-like rational quadratic trigonometric function with two form parameters. Since they are generated employing weights, the suggested rational quadratic trigonometric spline curve schemes are ...
Shamaila Samreen +4 more
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Sensors, 2022 This paper proposes a single-stage three-phase modular flyback differential inverter (MFBDI) for medium/high power solar PV grid-integrated applications.
Ahmed Ismail M. Ali +4 more
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