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    Wyświetlanie 1-8 z 8
    Tytuł:
    Solving of nonlinear equations which arise in collocation method
    Autorzy:
    Pilipczuk, Iwona
    Powiązania:
    https://bibliotekanauki.pl/articles/748354.pdf
    Data publikacji:
    1986
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Spectral, collocation and related methods
    Ill-posed problems
    Opis:
    .
    The paper concerns a Dirichlet problem for the equation - A.u + F(x,y,u,ux,Uy) = 0'on a rectangle. An iteration process for solving a nonlinear system of algebraic equations which arise in collocation method is considered. A convergence and an error estimate are obtained. Numerical results are presented for equations with F=cu+eu+f(x,y).
    Źródło:
    Mathematica Applicanda; 1986, 14, 27
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An algorithm for the solution of a linear system of algebraic equations arising in the mesh method for the Poisson equation
    Autorzy:
    Mejran, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/747553.pdf
    Data publikacji:
    1978
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Ill-posed problems,Direct methods for linear systems and matrix
    Opis:
    Artykuł nie zawiera streszczenia
    From the introduction: "We present an algorithm for direct (non-iterative) solution of the system of linear algebraic equations by the finite difference method for the equation Δu(x,y)=f(x,y), (x,y)∈Ω={(x,y):0<x,y<a,a>0}, u(x,y)=φ(x,y), (x,y)∈∂Ω. O(n2log2n) arithmetical operations are required for arbitrary f,φ, and O(n2) for some special ones, e.g., f≡0, φ arbitrary or φ≡0, f(x,y)≡h(x)g(x), where n is the number of unknowns in the system.''
    Źródło:
    Mathematica Applicanda; 1978, 6, 12
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Determination of selected parameters in a 1D open channel flow model
    Autorzy:
    Weinerowska-Bords, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1933161.pdf
    Data publikacji:
    2007
    Wydawca:
    Politechnika Gdańska
    Tematy:
    determination of parameters
    optimization procedures
    well-posed and ill-posed problems
    numerical methods
    Opis:
    Determination of the model's parameters is an important stage of mathematical models' application. In the case of a free-surface ID unsteady flow model defined by the de Saint- Venant equations, one of the groups of parameters to be estimated is the set of parameters describing energy losses due to friction. The parameters can be estimated in different ways, but in most cases the task of their determination is an ill-posed problem. In such cases, optimi-zation methods are the most common approach. In spite of numerous examples of such applications, these techniques are still not fully recognized, as there are several problems of different nature that require thorough analysis. Automatic optimization methods are discussed in the paper. The most important questions of choosing the objective function and the optimization algorithm are considered. Problems connected with data reliability and accessibility and their influence on the solution are discussed. The most common pitfalls of optimization applications are discussed. The analysis is supported with numerical examples.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2007, 11, 4; 341-364
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Choice of Subspace for Iterative Methods for Linear Discrete Ill-Posed Problems
    Autorzy:
    Calvetti, D.
    Lewis, B.
    Reichel, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908057.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda sprzężonych gradientów
    problem niewłaściwie postawiony
    minimal residual method
    conjugate gradient method
    ill-posed problems
    Opis:
    Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 5; 1069-1092
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A discrepancy principle for Tikhonov regularization with approximately specified data
    Autorzy:
    Thamban Nair, M.
    Schock, Eberhard
    Powiązania:
    https://bibliotekanauki.pl/articles/1294256.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    ill-posed problems
    minimal norm least-squares solution
    Moore-Penrose inverse
    Tikhonov regularization
    discrepancy principle
    optimal rate
    Opis:
    Many discrepancy principles are known for choosing the parameter α in the regularized operator equation $(T*T + αI)x_α^δ = T*y^δ$, $|y - y^δ| ≤ δ$, in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and $T*y^δ$ are approximated by Aₙ and $zₙ^δ$ respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable to the regularized projection method as well as to a degenerate kernel method considered by Groetsch (1990).
    Źródło:
    Annales Polonici Mathematici; 1998, 69, 3; 197-205
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    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:
    Misfit landforms imposed by ill-conditioned inverse parametric problems
    Autorzy:
    Łoś, M.
    Smołka, M.
    Schaefer, R.
    Sawicki, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/305739.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    taxonomy of ill-conditioned problems
    ill-posed global optimization problems
    fitness landscapes
    Opis:
    In this paper, we put forward a new topological taxonomy that allows us to distinguish and separate multiple solutions to ill-conditioned parametric inverse problems appearing in engineering, geophysics, medicine, etc. This taxonomy distinguishes the areas of insensitivity to parameters called the landforms of the misfit landscape, be it around minima (lowlands), maxima (uplands), or stationary points (shelves). We have proven their important separability and completeness conditions. In particular, lowlands, uplands, and shelves are pairwise disjoint, and there are no other subsets of the positive measure in the admissible domain on which the misfit function takes a constant value. The topological taxonomy is related to the second, “local” one, which characterizes the types of ill-conditioning of the particular solutions. We hope that the proposed results will be helpful for a better and more precise formulation of ill-conditioned inverse problems and for selecting and profiling complex optimization strategies used in solving these problems.
    Źródło:
    Computer Science; 2018, 19 (2); 157-178
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regularized penalty method for non-coercive parabolic optimal control problems
    Autorzy:
    Kaplan, A.
    Tichatschke, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/205538.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    distributed control
    ill-posed parabolic control problems
    penalty methods
    proximal point methods
    Opis:
    The application of a proximal point approach to illposed convex control problems governed by linear parabolic equations is studied. A stable penalty method is constructed by means of multi-step proximal regularization (only w.r.t. the control functions) in the penalized problems. For distributed control problems with state constraints convergence of the approximately determined solutions of the regularized problems to an optimal process is proved.
    Źródło:
    Control and Cybernetics; 1998, 27, 1; 5-27
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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