Results 261 to 270 of about 9,704 (289)
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Optimization Methods and Software, 2007
This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties
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This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties
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Generalized Lipschitz Functions
Computational Methods and Function Theory, 2006Lipschitz classes with variable exponents \(\text{Lip}_{\alpha(t)}\) are introduced. The exponents \({\alpha(t)}\) (called test functions) are supposed to be real-valued continuous functions defined in the right neighbourhood of zero satisfying the following conditions: \[ 1)\;{\alpha(t) = \alpha + o(1)},\;\alpha\in {\mathbb R};\quad 2) \;\int_{0}^{t} \
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International Journal of Computer Mathematics, 1995
Considered here is the problem of learning a nonlinear mapping with uncountable domain and range. The learning model used is that of piecewise linear interpolation on random samples from the domain. More specifically, a network learns a function by approximating its value, typically within some small ∈, when presented an arbitrary element of the domain.
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Considered here is the problem of learning a nonlinear mapping with uncountable domain and range. The learning model used is that of piecewise linear interpolation on random samples from the domain. More specifically, a network learns a function by approximating its value, typically within some small ∈, when presented an arbitrary element of the domain.
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Optimization of lipschitz continuous functions
Mathematical Programming, 1977This paper contains basic results that are useful for building algorithms for the optimization of Lipschitz continuous functionsf on compact subsets of En. In this settingf is differentiable a.e. The theory involves a set-valued mappingxźźźf(x) whose range is the convex hull of existing values of źf and limits of źf on a closedź-ball,B(x, ź).
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A lipschitz operator for function strips
Computing, 1986For function strips defined by an arithmetic interval expression, Lipschitz operators are constructed.
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Lipschitz Behavior and Characteristic Functions
SIAM Journal on Mathematical Analysis, 1973Let F be a distribution function. Its characteristic function belongs to ${\operatorname {Lip}}\alpha ,0 < \alpha < 1$, if and only if $F( - x)$ and $1 - F(x)$ are $O(x^{ - \alpha } )$ as $x \to \infty $ (see Boas [1]). The n-dimensional Fourier transform of a radial function reduces to the Hankel transform of a function in one variable.
Soni, K., Soni, R. P.
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Extensions of Continuous and Lipschitz Functions
Canadian Mathematical Bulletin, 2000AbstractWe show a result slightly more general than the following. Let K be a compact Hausdorff space, F a closed subset of K, and d a lower semi-continuous metric on K. Then each continuous function ƒ on F which is Lipschitz in d admits a continuous extension on K which is Lipschitz in d. The extension has the same supremum norm and the same Lipschitz
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MAKING CONTINUOUS FUNCTIONS LIPSCHITZ
Rocky Mountain Journal of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Artstein, Zvi, Beer, Gerald
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Extensions of Lipschitz Functions
Journal of the London Mathematical Society, 1974openaire +2 more sources
Lipschitz Continuity for Harmonic Functions and Solutions of the α¯-Poisson Equation
Axioms, 2023Miodrag Mateljević +2 more
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