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841.
Juan Carlos de los Reyes Irwin Yousept 《Journal of Mathematical Analysis and Applications》2009,356(1):257-279
The numerical solution of the Dirichlet boundary optimal control problem of the Navier-Stokes equations in presence of pointwise state constraints is investigated. Two different regularization techniques are considered. First, a Moreau-Yosida regularization of the problem is studied. Optimality conditions are derived and the convergence of the regularized solutions towards the original one is proved. A source representation of the control combined with a Lavrentiev type regularization strategy is also presented. The analysis concerning optimality conditions and convergence of the regularized solutions is carried out. In the last part of the paper numerical experiments are presented. For the numerical solution of each regularized problem a semi-smooth Newton method is applied. 相似文献
842.
This paper presents learning rates for the least-square regularized regression algorithms with polynomial kernels. The target
is the error analysis for the regression problem in learning theory. A regularization scheme is given, which yields sharp
learning rates. The rates depend on the dimension of polynomial space and polynomial reproducing kernel Hilbert space measured
by covering numbers. Meanwhile, we also establish the direct approximation theorem by Bernstein-Durrmeyer operators in with Borel probability measure.
相似文献
843.
We are interested in minimizing functionals with ℓ2 data and gradient fitting term and ℓ1 regularization term with higher order derivatives in a discrete setting. We examine the structure of the solution in 1D by
reformulating the original problem into a contact problem which can be solved by dual optimization techniques. The solution
turns out to be a ’smooth’ discrete polynomial spline whose knots coincide with the contact points while its counterpart in
the contact problem is a discrete version of a spline with higher defect and contact points as knots. In 2D we modify Chambolle’s
algorithm to solve the minimization problem with the ℓ1 norm of interacting second order partial derivatives as regularization term. We show that the algorithm can be implemented
efficiently by applying the fast cosine transform. We demonstrate by numerical denoising examples that the ℓ2 gradient fitting term can be used to avoid both edge blurring and staircasing effects.
相似文献
844.
S. A. Modina 《Russian Mathematics (Iz VUZ)》2009,53(4):31-33
In this paper we study the three-element functional equation , subject to We assume that the coefficients G(z) and g(z) are holomorphic in R and their boundary values G +(t) and g +(t) belong to H(Γ), G(t)G(t ?1) = 1. We seek for solutions Φ(z) in the class of functions holomorphic outside of \(\bar R\) such that they vanish at infinity and their boundary values Φ?(t) also belong to H(Γ). Using the method of equivalent regularization, we reduce the problem to the 2nd kind integral Fredholm equation.
相似文献
$(V\Phi )(z) \equiv \Phi (iz) + \Phi ( - iz) + G(z)\Phi \left( {\frac{1}{z}} \right) = g(z), z \in R,$
$R: = \{ z:\left| z \right| < 1, \left| {\arg z} \right| < \frac{\pi }{4}\} .$
845.
M. A. Korotkii 《Russian Mathematics (Iz VUZ)》2009,53(2):68-73
We consider the problem of the reconstruction of an a priori unknown control in a dynamic system based on approximate a posteriori observations of the motion of this system. We propose to solve this problem by the Tikhonov method with a stabilizer which contains the total variation of the control. This provides the piecewise uniform convergence of regularized approximations and thus enables one to numerically reconstruct the fine structure of the desired solution. 相似文献
846.
Stefania Bellavia Jacek Gondzio Benedetta Morini 《Numerical Linear Algebra with Applications》2009,16(1):39-61
A regularized Newton‐like method for solving nonnegative least‐squares problems is proposed and analysed in this paper. A preconditioner for KKT systems arising in the method is introduced and spectral properties of the preconditioned matrix are analysed. A bound on the condition number of the preconditioned matrix is provided. The bound does not depend on the interior‐point scaling matrix. Preliminary computational results confirm the effectiveness of the preconditioner and fast convergence of the iterative method established by the analysis performed in this paper. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
847.
We consider a linear system of the form A1x1+ A2x2+η=b1. The vector η consists of identically distributed random variables all with mean zero. The unknowns are split into two groups x1 and x2. In the model usually there are more unknowns than observations and the resulting linear system is most often consistent having an infinite number of solutions. Hence some constraint on the parameter vector x is needed. One possibility is to avoid rapid variation in, e.g. the parameters x2. We formulate the problem as a partially regularized least‐squares problem, and propose a direct solution method based on the QR decomposition of matrix blocks. Further we consider regularizing using one and two regularization parameters, respectively. We also discuss the choice of regularization parameters, and extend Reinsch's method to the case with two parameters. Also the cross‐validation technique is treated. We present test examples taken from an application in modelling of the substance transport in rivers. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
848.
849.
Nguyen Buong 《Computational Mathematics and Mathematical Physics》2006,46(3):354-360
An operator regularization method is considered for ill-posed vector optimization of weakly lower semicontinuous essentially
convex functionals on reflexive Banach spaces. The regularization parameter is chosen by a modified generalized discrepancy
principle. A condition for the estimation of the convergence rate of regularized solutions is derived.
This article was submitted by the author in English. 相似文献
850.
Pallavi Mahale 《Numerical Functional Analysis & Optimization》2013,34(11):1448-1470
Recently, Mahale and Nair considered a simplified generalized Gauss-Newton iterative method for getting an approximate solution for the nonlinear ill-posed operator equation under the modified general source condition. The advantage of this method and the source condition over the classical Gauss-Newton iterative method is that the iterations and source condition involve calculation of the Fréchet derivative only at the point x 0, i.e., at the initial approximation for the exact solution x ? of the nonlinear ill-posed operator equation F(x) = y. Motivated by the work of Qinian Jin and Tautenhan, error analysis of the simplified Gauss-Newton iterative method is done in this article under a Morozove-type stopping rule, which is much simpler than the stopping rule considered in the article of Mahale and Nair. An order optimal error estimate is obtained under a modified general source condition which also involves calculation of the Fréchet derivative at the point x 0. 相似文献