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Identification of critical curves. II. Discretization and numerical realization

Jaroslav Haslinger, Václav Horák, Pekka Neittaanmäki, Kimmo Salmenjoki (1991)

Applications of Mathematics

We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.

Identification of parameters in initial value problems for ordinary differential equations

Chleboun, Jan, Mikeš, Karel (2015)

Programs and Algorithms of Numerical Mathematics

Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically...

Identification of source term in a nonlinear degenerate parabolic equation with memory

Soufiane Abid, Khalid Atifi, El-Hassan Essoufi, Abderrahim Zafrar (2024)

Applications of Mathematics

In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness...

Identification problem for nonlinear beam -- extension for different types of boundary conditions

Radová, Jana, Machalová, Jitka (2023)

Programs and Algorithms of Numerical Mathematics

Identification problem is a framework of mathematical problems dealing with the search for optimal values of the unknown coefficients of the considered model. Using experimentally measured data, the aim of this work is to determine the coefficients of the given differential equation. This paper deals with the extension of the continuous dependence results for the Gao beam identification problem with different types of boundary conditions by using appropriate analytical inequalities with a special...

Image Compression with Schauder Bases

Zbigniew Ciesielski (2001)

Applicationes Mathematicae

As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...

Image segmentation with a finite element method

Blaise Bourdin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation...

Improved local convergence analysis of inexact Newton-like methods under the majorant condition

Ioannis K. Argyros, Santhosh George (2015)

Applicationes Mathematicae

We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.

Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

N.U. Ahmed (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

Increasing pursuer capturability by using hybrid dynamics

Valery Y. Glizer, Vladimir Turetsky (2015)

International Journal of Applied Mathematics and Computer Science

A robust interception of a maneuverable target (evader) by an interceptor (pursuer) with hybrid dynamics is considered. The controls of the pursuer and the evader are bounded. The duration of the engagement is prescribed. The pursuer has two possible dynamic modes, which can be switched once during the engagement, while the dynamics of the evader are fixed. The case where for both dynamic modes there exists an unbounded capture zone was analyzed in our previous work. The conditions under which the...

Inégalité isopérimétrique et calibration

Frédéric Helein (1994)

Annales de l'institut Fourier

On montre que l’inégalité isopérimétrique pour un domaine dans le plan euclidien, la sphère de dimension 2, ou l’espace hyperbolique de dimension 2, peut s’obtenir à l’aide d’une calibration.

Inégalités variationnelles non convexes

Messaoud Bounkhel, Djalel Bounkhel (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.

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