TITLE

On the a posteriori choice of a regularization parameter in the solution of severely ill-posed problems

AUTHOR(S)
Solodky, Sergei; Grushevaya, Anna
PUB. DATE
February 2012
SOURCE
Journal of Mathematical Sciences;Feb2012, Vol. 181 Issue 1, p98
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider the problem of approximate solution of severely ill-posed problems with perturbed right-hand sides. The approximation properties of a finite-dimensional version of the Tikhonov regularization in the combination with the a posteriori choice of a regularization parameter by means of the balancing principle are analyzed. It is shown that this approach provides an optimal order of accuracy. The efficiency of the theoretical results is checked by comparison with the earlier known methods.
ACCESSION #
71509049

 

Related Articles

  • Flexible-attribute problems. Mihelič, Jurij; Robič, Borut // Computational Optimization & Applications;Nov2010, Vol. 47 Issue 3, p553 

    Problems with significant input-data uncertainty are very common in practical situations. One approach to dealing with this uncertainty is called scenario planning, where the data uncertainty is represented with scenarios. A scenario represents a potential realization of the important parameters...

  • Optimal cooling strategies in polymer crystallization. Escobedo, Ramón; Fernández, Luis // Journal of Mathematical Chemistry;Feb2012, Vol. 50 Issue 2, p313 

    An optimal control problem for cooling strategies in polymer crystallization processes described by a deterministic model is solved in the framework of a free boundary problem. The strategy of cooling both sides of a one dimensional sample is introduced for the first time in this model, and is...

  • Numerical Identification of Multiparameters in the Space Fractional Advection Dispersion Equation by Final Observations. Dali Zhang; Gongsheng Li; Guangsheng Chi; Xianzheng Jia; Huiling Li // Journal of Applied Mathematics;2012, p1 

    This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the...

  • Smooth finite-dimensional approximations of distributed optimization problems via control discretization. Chernov, A. // Computational Mathematics & Mathematical Physics;Dec2013, Vol. 53 Issue 12, p1839 

    Approximating finite-dimensional mathematical programming problems are studied that arise from piecewise constant discretization of controls in the optimization of distributed systems of a fairly broad class. The smoothness of the approximating problems is established. Gradient formulas are...

  • Two-dimensional regular C -fractions. Kuchmins'ka, Kh. // Journal of Mathematical Sciences;Aug2013, Vol. 192 Issue 5, p485 

    We consider one of the types of functional two-dimensional continued fractions corresponding to a formal double power series. Using estimates for the remainders of a two-dimensional continued fraction, the relation for the difference between two approximants of a two-dimensional continued...

  • RECOVERY OF THE LOCAL VOLATILITY FUNCTION USING REGULARIZATION AND A GRADIENT PROJECTION METHOD. QINGHUA MA; ZUOLIANG XU; LIPING WANG // Journal of Industrial & Management Optimization;Apr2015, Vol. 11 Issue 2, p421 

    This paper considers the problem of calibrating the volatility function using regularization technique and the gradient projection method from given option price data. It is an ill-posed problem because of at least one of three well-posed conditions violating. We start with the European option...

  • On DC optimization algorithms for solving minmax flow problems. Muu, Le; Thuy, Le // Mathematical Methods of Operations Research;Aug2014, Vol. 80 Issue 1, p83 

    We formulate minmax flow problems as a DC optimization problem. We then apply a DC primal-dual algorithm to solve the resulting problem. The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems.

  • A New Dominance Method Based on Expanding Dominated Area for Many-Objective Optimization. Liu, Junhua; Wang, Yuping; Wang, Xingyin; Guo, Si; Sui, Xin // International Journal of Pattern Recognition & Artificial Intell;Mar2019, Vol. 33 Issue 3, pN.PAG 

    The performance of the traditional Pareto-based evolutionary algorithms sharply reduces for many-objective optimization problems, one of the main reasons is that Pareto dominance could not provide sufficient selection pressure to make progress in a given population. To increase the selection...

  • Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations. Van Ngai, Huynh; Tinh, Phan Nhat // Mathematics of Operations Research;Aug2015, Vol. 40 Issue 3, p703 

    Metric subregularity and regularity of multifunctions are fundamental notions in variational analysis and optimization. Using the concept of strong slope, in this paper we first establish a criterion for metric subregularity of multifunctions between metric spaces. Next, we use a combination of...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics