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Optimal approximation by piecewise smooth functions and associated variational problems

by David Mumford - Commun. Pure Applied Mathematics , 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
Abstract - Cited by 1294 (14 self) - Add to MetaCart
(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems

Smooth minimization of nonsmooth functions

by Yu. Nesterov - Math. Programming , 2005
"... In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization. F ..."
Abstract - Cited by 523 (1 self) - Add to MetaCart
In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization

Approximation of partially smooth functions

by John Erik Fornæss, Yinxia Wang, Erlend Fornæss Wold - PROCEEDINGS OF QIKENG LU CONFERENCE, JUNE 2006, SCIENCE IN CHINA (SER A , 2007
"... In this paper we discuss approximation of partially smooth functions by smooth functions. This problem arises naturally in the study of laminated currents. ..."
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In this paper we discuss approximation of partially smooth functions by smooth functions. This problem arises naturally in the study of laminated currents.

Adapting to unknown smoothness via wavelet shrinkage

by David L. Donoho, Iain M. Johnstone - JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION , 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
Abstract - Cited by 1006 (18 self) - Add to MetaCart
We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level

Projection Pursuit Regression

by Jerome H. Friedman, Werner Stuetzle - Journal of the American Statistical Association , 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general- smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
Abstract - Cited by 550 (6 self) - Add to MetaCart
A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general- smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures

Mixed optimization for smooth functions

by Mehrdad Mahdavi , Lijun Zhang , Rong Jin - In Neural Information Processing Systems (NIPS , 2013
"... Abstract It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/ √ T ), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a conve ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
Abstract It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/ √ T ), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a

ON ISOMORPHISMS OF ALGEBRAS OF SMOOTH FUNCTIONS

by Janez Mrčun , 2003
"... Abstract. We show that for any smooth paracompact Hausdorff manifolds M and N, which are not necessarily second countable or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on M is given by composition with a unique diffeomorp ..."
Abstract - Cited by 12 (0 self) - Add to MetaCart
Abstract. We show that for any smooth paracompact Hausdorff manifolds M and N, which are not necessarily second countable or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on M is given by composition with a unique

Reconstruction and Representation of 3D Objects with Radial Basis Functions

by J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, T. R. Evans - Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH , 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
Abstract - Cited by 505 (1 self) - Add to MetaCart
We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs

High Accuracy Optical Flow Estimation Based on a Theory for Warping

by Thomas Brox, Andrés Bruhn, Nils Papenberg, Joachim Weickert , 2004
"... We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint. ..."
Abstract - Cited by 509 (45 self) - Add to MetaCart
We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint.

STABILIZERS AND ORBITS OF SMOOTH FUNCTIONS

by Sergey Maksymenko , 2005
"... Abstract. Let f: Rm → R be a smooth function such that f(0) = 0. We give a condition on f when for arbitrary preserving orientation diffeomorphism φ: R → R such that φ(0) = 0 the function φ ◦ f is right equivalent to f, i.e.there exists a diffeomorphism h: Rm → Rm such that φ ◦ f = f ◦ h at 0 ∈ Rm ..."
Abstract - Cited by 6 (6 self) - Add to MetaCart
Abstract. Let f: Rm → R be a smooth function such that f(0) = 0. We give a condition on f when for arbitrary preserving orientation diffeomorphism φ: R → R such that φ(0) = 0 the function φ ◦ f is right equivalent to f, i.e.there exists a diffeomorphism h: Rm → Rm such that φ ◦ f = f ◦ h at 0
Results 1 - 10 of 18,705