Results 11 to 20 of about 1,759 (215)
Segment Tracing Using Local Lipschitz Bounds [PDF]
Computer Graphics Forum, 2020 AbstractWe introduce Segment Tracing, a new algorithm that accelerates the classical Sphere Tracing method for computing the intersection between a ray and an implicit surface. Our approach consists in computing the Lipschitz bound locally over a segment to improve the marching step computation and accelerate the overall process.
Galin, Eric +3 more
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Characterization of the Local Lipschitz Constant
Journal of Approximation Theory, 1994 Let \(X\) be a closed subset of \([a,b]\) with at least \(n+1\) points, and let \(C(X)\) denote the space of continuous real valued functions on \(X\) endowed with the uniform norm. Let \(H_ n\) denote a Haar set of dimension \(n\), and let the best approximation of \(f\in C(X)\) in \(H_ n\) be \(B_ n(f)\).
Bartelt, M. W., Swetits, J. J.
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Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by the p(x)-Laplacian
The Scientific World Journal, 2013 A class of nonlinear Neumann problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions.
Qing-Mei Zhou
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Journal of Approximation Theory, 1985 Let X be a closed subset of \(I=[-1,1]\). For \(f\in C[X]\), the local Lipschitz constant is defined to be \(\lambda_{n\delta}(f)=\sup \{\| B_ n(f)-B_ n(g)\| /\| f-g ...
Angelos, James R +3 more
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Nonsmooth analysis and optimization on partially ordered vector spaces
International Journal of Mathematics and Mathematical Sciences, 1992 Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector
Thomas W. Reiland
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The oscillation of separately locally Lipschitz functions
Karpatsʹkì Matematičnì Publìkacìï, 2013 We prove that a function which dened on the product of two metric Baire spaces is the oscillation of some separately locally Lipschitz function if and only if it is an upper semicontinuous non-negative function which has a crosswise nowhere dense closure
V. H. Herasymchuk, O. V. Maslyuchenko
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A NEW PROOF OF CLARKE'S THEOREM
Tạp chí Khoa học Đại học Đà Lạt, 2012 In this paper, we give a new proof of the theorem of Clarke on Fritz John optimality conditions for nonsmooth optimisation problems involving locally Lipschitz functions.
Gue Myung Lee, Phạm Tiến Sơn
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Hybrid robust observers for locally Lipschitz systems [PDF]
2009 European Control Conference (ECC), 2009 State observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach applicable to nonlinear systems with bounded solutions.
Bobtsov, Alexey, Efimov, Denis
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Local and global Lipschitz constants
Journal of Approximation Theory, 1986 Let X be a closed subset of [-1,1] which contains at least \(n+2\) points, and let \(B_ n(f)\) be the best uniform approximation to \(f\in C[X]\) from the set \(\pi_ n\) of all polynomials of degree at most n. The global Lipschitz constant of f is defined as \[ \lambda_ n(f)=\sup \{\| B_ n(f)-B_ n(g)\| /\| f-g\|:g\in C[X],g\neq f\}, \] and the strong ...
Angelos, James R +4 more
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Regularity of Generalized Mean-Field G-SDEs
MathematicsWe study the regularity properties of the unique solution of a generalized mean-field G-SDE. More precisely, we consider a generalized mean-field G-SDE with a square-integrable random initial condition, establish its first- and second-order Fréchet ...
Karl-Wilhelm Georg Bollweg +1 more
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