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    Wyświetlanie 1-6 z 6
    Tytuł:
    The finite difference approximation for the Dirichlet problem with a non-uniform mesh on a boundary
    Autorzy:
    Morawiec, Grażyna
    Powiązania:
    https://bibliotekanauki.pl/articles/747719.pdf
    Data publikacji:
    1987
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Derivation of finite difference approximations
    Error bounds
    Opis:
    .
    The author describes a construction of the positive difference scheme, which is the approximation of the Dirichlet problem for an elliptic second order equation with mixed derivatives in an arbitrary region in R2. The a priori estimation for the approximate solution is proved and the estimation of the rate of convergence in maximum norm is established.
    Źródło:
    Mathematica Applicanda; 1987, 16, 30
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inequality-Based Approximation of Matrix Eigenvectors
    Autorzy:
    Kocsor, A.
    Dombi, J.
    Balint, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/908503.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    matematyka
    eigenvectors
    eigenvalues
    inequalities
    error bounds
    iterative methods
    Opis:
    A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 4; 533-538
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Effective difference schemes for the heat equation in arbitrary regions
    Autorzy:
    Dryja, Maksymilian
    Powiązania:
    https://bibliotekanauki.pl/articles/748525.pdf
    Data publikacji:
    1982
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Stability and convergence of difference methods,Error bounds
    Opis:
    .
    In this paper the author considers the problem of the heat equation ∂u/∂t−(∂2u/∂x21+∂2u/∂x22)=f(x,t) for x∈Ω and t∈(0,T], u(x,0)=φ(x) for x∈Ω, u(x,t)=0 for x∈∂Ω and t∈[0,T]. He constructs a Crank-Nicolson and an alternating direction difference scheme on a regular mesh with steps hi (i=1,2) and τ. Linear interpolation is used for the approximation of the boundary condition. Besides stability of both schemes error estimates are derived under the condition that the derivatives ∂5u/∂t∂x4i and ∂3u/∂t3 are bounded. These estimates are: maxn∥un−yn∥A≤M(τ2+h3/2)andmaxn∥un−yn∥h≤M(τ2+h2+τh1/2+h5/2/τ). Here h=max(h1,h2), un=u(⋅,nτ), yn is the approximate value of un, ∥u∥2h=(u,u)h, (u,v)h=h1h2∑x∈Ωhu(x)v(x) (Ωh is the set of all mesh points lying in Ω), and ∥u∥2A=(u,Au)h where A is the discrete Laplace operator.
    Źródło:
    Mathematica Applicanda; 1982, 10, 19
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error bounds for convex constrained systems in Banach spaces
    Autorzy:
    Song, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/970243.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    przestrzeń Banacha
    error bounds
    constrained convex system
    set-valued mapping
    Banach space
    Opis:
    In this paper, we first establish both primal (involving directional derivatives and tangent cones) and dual characterizations (involving subdifferential and normal cones) for the local (global) error bounds of constrained set-valued systems; as an application, we then derive both primal and dual characterizations for the local (global) error bounds of the constrained convex inequality systems in a general Banach space and also some sufficient conditions. The obtained results improve or generalize some known results.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 775-792
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak sharp minima revisited Part I : basic theory
    Autorzy:
    Burke, J.
    Deng, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/206183.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dwoistość
    funkcja recesji
    ograniczenie błędu
    stożek recesji
    boundedly weak sharp minima
    duality
    error bounds
    normal cone inclusion
    recession cone
    recession function
    weak sharp minima
    Opis:
    The notion of sharp minima, or strongly unique local minima, emerged in the late 1970's as an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. The work of Cromme and Polyak is of particular importance in this development. In the late 1980's Ferris coined the term weak sharp minima to describe the extension of the notion of sharp minima to include the possibility of a non-unique solution set. This notion was later extensively studied by many authors. Of particular note in this regard is the paper by Burke and Ferrris which gives an extensive exposition of the notion and its impact on convex programming and convergence analysis in finite dimensions. In this paper we build on the work of Burke and Ferris. Specifically, we generalize their work to the normed linear space setting, further dissect the normal cone inclusion characterization for weak sharp minima, study the asymptotic properties of weak sharp minima in terms of associated recession functions, and give new characterizations for local weak sharp minima and boundely weak sharp minima. This paper is the first of a two part work on this subject. In Part II, we study the links between the notions of weak sharp minima, bounded linear regularity, linear regularity, metric regularity, and error bounds in convex programming. Along the way, we obtain both new results and reproduce many existing results from a fresh perspective.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 439-469
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross–Pitaevskii equation
    Autorzy:
    Hendy, Ahmed S.
    Macías-Díaz, Jorge E.
    Powiązania:
    https://bibliotekanauki.pl/articles/330834.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    generalized Gross–Pitaevskii system
    Riesz fractional diffusion
    Sobolev inequality
    conservative method
    optimal error bounds
    równanie Grossa-Pitaevskiego
    nierówność Sobolewa
    metoda konserwatywna
    optymalna granica błędu
    Opis:
    The present work departs from an extended form of the classical multi-dimensional Gross–Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross–Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 4; 713-723
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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