Restricted Nonlinear Approximation

Cohen, A.; DeVore, R. A.; Hochmuth, R.
January 2000
Constructive Approximation;Jan2000, Vol. 16 Issue 1, p85
Academic Journal
We introduce a new form of nonlinear approximation called restricted approximation . It is a generalization of n -term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of L[sub p] and Besov spaces. We characterize, both in terms of their wavelet coefficients and also in terms of their smoothness, the functions which are approximated with a specified rate by restricted approximation. We also show the relation of this form of approximation with certain types of thresholding of wavelet coefficients.


Related Articles

  • About right.  // New Scientist;12/22/90, Vol. 128 Issue 1748, p90 

    Comments on the study of approximation.

  • Physical and mathematical content of coupled-cluster equations. IV. Impact of approximations to... Jankowski, K.; Kowalski, K. // Journal of Chemical Physics;8/15/1999, Vol. 111 Issue 7, p2952 

    Studies the impact of approximations to the form of the cluster operator on the structure and physical significance of the complete set of geometrically isolated solutions to the coupled-cluster (CC) equations. Correspondence of solutions obtained at various levels of the approximation process;...

  • The Besicovitch covering theorem and near-minimizers for the couple (L2;BV). Asekritova, Irina; Kruglyak, Natan // Proceedings of the Estonian Academy of Sciences;2010, Vol. 59 Issue 1, p29 

    Let Ω be rectangle in R2. A new algorithm for the construction of a near-minimizer for the couple (L2(Ω),BV(Ω)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f ∈ L2(Ω).

  • [InlineMediaObject not available: see fulltext.]-Matrix Arithmetics in Linear Complexity. B�rm, S. // Computing;Feb2006, Vol. 77 Issue 1, p1 

    For hierarchical matrices, approximations of the matrix-matrix sum and product can be computed in almost linear complexity, and using these matrix operations it is possible to construct the matrix inverse, efficient preconditioners based on approximate factorizations or solutions of certain...

  • Direct Approximation Theorem on a Family of Two Segments. Mezhevich, K.G.; Shirokov, N.A. // Journal of Mathematical Sciences;Jul2004, Vol. 122 Issue 3, p3246 

    Polynomial approximations are studied for some function classes. Bibliography: 6 titles.

  • Characterization of Periodic L1-Unicity Subspaces. Sommer, Manfred // Constructive Approximation;2005, Vol. 22 Issue 1, p95 

    We are interested in characterizing the finite-dimensional subspaces of periodic, real-valued, and continuous functions which admit uniqueness of weighted best L1-approximations. Considering the cases of odd and even dimension separately, we are able to give intrinsic characterizations of...

  • Domain wall motion in ferromagnets modelled by a quintic complex Ginzburg-Landau equation. Nguenang, J. -P.; Njassap Njassap, T.; Kofan�, T. C. // European Physical Journal B -- Condensed Matter;Sep2008, Vol. 65 Issue 4, p539 

    A quintic complex Ginzburg-Landau equation is derived from a Landau-Lifshitz-Gilbert equation and is used to describe the magnetization dynamics in a one-dimensional uni-axial ferromagnet. Trough the use of suitable approximations, we derive the magnetic solitary wave excitations solutions which...

  • Queues with Many Servers and Impatient Customers. Mandelbaum, Avishai; Momčilović, Petar // Mathematics of Operations Research;Feb2012, Vol. 37 Issue 1, p41 

    The asymptotic many-server queue with abandonments, G=GI=N C GI, is considered in the quality- and efficiency-driven (QED) regime. Here the number of servers and the offered load are related via the square-root rule, as the number of servers increases indefinitely. QED performance entails short...

  • A primal-dual approximation algorithm for stochastic facility location problem with service installation costs. Wang, Xing; Xu, Dachuan; Zhao, Xinyuan // Frontiers of Mathematics in China;Oct2011, Vol. 6 Issue 5, p957 

    We consider the stochastic version of the facility location problem with service installation costs. Using the primal-dual technique, we obtain a 7-approximation algorithm.


Read the Article


Sign out of this library

Other Topics