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Wyświetlanie 1-15 z 56
Tytuł:
Regularization and discretization of linear-quadratic control problems
Autorzy:
Alt, W.
Seydenschwanz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206162.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
bang-bang control
regularization
discretization
Opis:
We analyze regularizations of a class of linear-quadratic optimal control problems with control appearing linearly. It is shown that if the optimal control is bang-bang or if a coercivity condition for the state variables is satisfied, the solutions are continuous functions of the regularization parameter. Combining error estimates for Euler discretizations of the regularized problems with those for the regularization error, we choose the regularization parameter in dependence of the meshsize to obtain optimal convergence rates for the discrete solutions. Numerical experiments confirm the theoretical findings.
Źródło:
Control and Cybernetics; 2011, 40, 4; 903-920
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On regularization in superreflexive Banach spaces by infimal convolution formulas
Autorzy:
Cepedello-Boiso, Manuel
Powiązania:
https://bibliotekanauki.pl/articles/1218460.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
regularization in Banach spaces
convex functions
Opis:
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex $C^{1,α}$ functions converging to f uniformly on bounded sets and preserving the infimum and the set of minimizers of f. The techniques we develop are based on the use of extended inf-convolution formulas and convexity properties such as the preservation of smoothness for the convex envelope of certain differentiable functions.
Źródło:
Studia Mathematica; 1998, 129, 3; 265-284
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization of Coulomb potential for calculating electron density in quantum mechanical systems
Autorzy:
Kshevetskty, S.
Shapilov, A.
Powiązania:
https://bibliotekanauki.pl/articles/1940700.pdf
Data publikacji:
2017
Wydawca:
Politechnika Gdańska
Tematy:
regularization
Coulomb potential
electron density
Opis:
In this paper we show a simple and effective method for regularizing the Coulomb potential for numerical calculations of quantum mechanical problems, such as, for example, the solution of the Schrödinger equation, the expansion of charge density and others. The introduction explains why the regularization of the Coulomb potential is important. In the second part, the regularization method itself as well as its advantages and disadvantages will be described in detail. The third part demonstrates some numerical calculations for the Sulfur + Hydrogen system using the proposed method. In the final part, the obtained results are summed up.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2017, 21, 2; 177-184
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks on best regularization
Autorzy:
Friedrich, V.
Powiązania:
https://bibliotekanauki.pl/articles/720916.pdf
Data publikacji:
1984
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Banach Center Publications; 1984, 13, 1; 719-724
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization parameter selection in discrete ill-posed problems—The use of the U-curve
Autorzy:
Krawczyk-Stańdo, D.
Rudnicki, M.
Powiązania:
https://bibliotekanauki.pl/articles/929617.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
problem niewłaściwie postawiony
regularyzacja Tichonowa
parametr regularyzacji
ill-posed problems
Tikhonov regularization
regularization parameter
L-curve
U-curve
Opis:
To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter \alfa we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter \alfa, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 2; 157-164
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints
Autorzy:
Neitzel, I.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970314.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear parabolic equation
pointwise state constraints
Moreau-Yosida regularization
Lavrentiev regularization
convergence
strong regularity
local uniqueness
Opis:
Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.
Źródło:
Control and Cybernetics; 2008, 37, 4; 1013-1043
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptation of the Regularization Parameters in the Nm-Delta Networks
Autorzy:
Gołąbek, P.
Kosiński, W.
Powiązania:
https://bibliotekanauki.pl/articles/911150.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
regularyzacja
Levenberg-Marquardt
NM-Delta
M-Delta
regularization
quasi-Newton
Opis:
The paper describes an application of regularization techniques to an automatic choice of parameters driving the learning process in the NM-Delta neural network architecture. The heterogeneous learning algorithm is identified as very similar to the Levenberg-Marquardt method but with a considerably smaller computational cost and different justification of parameter selection. The performance of the modified algorithm proves to be comparable with that of the Levenberg-Marquardt.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2000, 10, 4; 779-790
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Evaluation of nonlinear constants from results of acoustic measurements. Regularization of problem
Autorzy:
Leble, S. B.
Vereshchagin, D. A.
Vereshchagina, I. S.
Powiązania:
https://bibliotekanauki.pl/articles/332067.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Akustyczne
Tematy:
acoustic measurements
regularization
Opis:
The method of nonlinear constants B/A and C/A determination is discussed. It bases on comparison of experimental results of acoustic signal propagation with results of theoretical investigation of this problem. It is shown, that this problem, in general case, is ill-posed. So we use methods of ill-posed problem solution regularization. The values of the constants, which were extracted using this method, are in good accordance with estimations by other authors.
Źródło:
Hydroacoustics; 2003, 6; 159-166
1642-1817
Pojawia się w:
Hydroacoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the regularization error of state constrained Neumann control problems
Autorzy:
Krumbiegel, K.
Rosch, A.
Powiązania:
https://bibliotekanauki.pl/articles/969594.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
elliptic equation
state constraints
boundary control
regularization
virtual control
Opis:
A linear elliptic optimal control problem with point-wise state constraints in the interior of the domain is considered. Furthermore, the control is given on the boundary with associated constraints. An artificial distributed control is introduced in the cost functional, in the state equation and in the state constraints. Since there are no control constraints for the artificial control, efficient numerical methods can be easily established. Based on a possible violation of the pure pointwise state constraints, an error estimate for the regularization error is derived. The theoretical results are illustrated by numerical tests.
Źródło:
Control and Cybernetics; 2008, 37, 2; 369-392
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Performance analysis of regularization algorithms used for image reconstruction in computed tomography
Autorzy:
Wysoczański, D.
Mroczka, J.
Polak, A. G.
Powiązania:
https://bibliotekanauki.pl/articles/201356.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
computed tomography
image reconstruction
algebraic approach
regularization methods
Opis:
Computed tomography is one of the most significant diagnostic techniques in medicine. This work is focused on hard-field imaging, where signals take a form of straight rays and the reconstructed image can be presented as a matrix with unknown pixels. Algebraic methods for direct computation of the image have not been used in practice because of the scale of the problem and numerical errors appearing in the solution. The aim of this work was to analyse the performance of direct algebraic algorithms for tomographic image reconstruction including regularisation mechanism such as: generalised regularisation, Tikhonov regularisation, Twomey regularisation and ridge regression (RR), as well as comparing the results with the filtered backprojection (FBP) as the reference method. The performed analyses demonstrated that the regularised algebraic methods are more accurate than the commonly used FBP, and RR appeared the most precise among them. Additionally it was shown that the invariant system matrix (inverted during calculations) can be easily determined by solving the forward problem. Finally, potential directions of further research have been pointed out.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 467-474
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization of non-coercive quasi variational inequalities
Autorzy:
Giannessi, F.
Khan, A.
Powiązania:
https://bibliotekanauki.pl/articles/205586.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
operator monotoniczny i pseudomonotoniczny
zbieżność
convergence
monotone and pseudo-monotone operators
non-coercive
quasi-variational inequalities
regularization
Opis:
This paper is devoted to the regularization of quasi-variational inequalities. The quasi-variational inequality is considered with multivalued operator. The operator involved is taken to be non-coercive and the data are assumed to be known approximately only. Under the assumption that the quasi-variational inequality be solvable, a weakly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method.
Źródło:
Control and Cybernetics; 2000, 29, 1; 91-110
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens
Autorzy:
Nosich, A.I.
Powiązania:
https://bibliotekanauki.pl/articles/309580.pdf
Data publikacji:
2001
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
wave scattering
imperfect boundary conditions
thin screens
regularization
Opis:
The paper is focussed on the development of the method of analytical regularization (MAR) in electromagnetic wave scattering and absorption by imperfect scatterers shaped as thin screens.
Źródło:
Journal of Telecommunications and Information Technology; 2001, 3; 72-79
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints
Autorzy:
Wachsmuth, D.
Wachsmuth, G.
Powiązania:
https://bibliotekanauki.pl/articles/206129.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
source condition
discrepancy principle
nonsmooth optimization
convex constraints
sparsity
regularization error estimates
Opis:
In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive a-priori regularization error estimates if the regularization parameter as well as the noise level tend to zero. We rely on an assumption that is a combination of a source condition and of a structural assumption on the active sets. Moreover, we introduce a strategy to choose the regularization parameter in dependence of the noise level. We prove convergence of this parameter choice rule with optimal order.
Źródło:
Control and Cybernetics; 2011, 40, 4; 1125-1158
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Tikhonov regularization and constrained quadratic programming for magnetic coil design problems
Autorzy:
Garda, B.
Galias, Z.
Powiązania:
https://bibliotekanauki.pl/articles/330150.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
coil design problem
constrained quadratic programming
Tikhonov regularization
projektowanie cewki
programowanie kwadratowe
regularyzacja Tikhonova
Opis:
In this work, the problem of coil design is studied. It is assumed that the structure of the coil is known (i.e., the positions of simple circular coils are fixed) and the problem is to find current distribution to obtain the required magnetic field in a given region. The unconstrained version of the problem (arbitrary currents are allowed) can be formulated as a Least-SQuares (LSQ) problem. However, the results obtained by solving the LSQ problem are usually useless from the application point of view. Moreover, for higher dimensions the problem is ill-conditioned. To overcome these difficulties, a regularization term is sometimes added to the cost function, in order to make the solution smoother. The regularization technique, however, produces suboptimal solutions. In this work, we propose to solve the problem under study using the constrained Quadratic Programming (QP) method. The methods are compared in terms of the quality of the magnetic field obtained, and the power of the designed coil. Several 1D and 2D examples are considered. It is shown that for the same value of the maximum current the QP method provides solutions with a higher quality magnetic field than the regularization method.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 249-257
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 56

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