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    Wyświetlanie 1-11 z 11
    Tytuł:
    Convergence Analysis of An Improved Extreme Learning Machine Based on Gradient Descent Method
    Autorzy:
    Yusong, L.
    Zhixun, S.
    Bingjie, Y.
    Xiaoling, G.
    Zhaoyang, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/972914.pdf
    Data publikacji:
    2016
    Wydawca:
    Społeczna Akademia Nauk w Łodzi
    Tematy:
    neural networks
    monotonicity
    weak convergence
    strong convergence
    USUA
    MNIST
    Opis:
    Extreme learning machine (ELM) is an efficient algorithm, but it requires more hidden nodes than the BP algorithms to reach the matched performance. Recently, an efficient learning algorithm, the upper-layer-solution-unaware algorithm (USUA), is proposed for the single-hidden layer feed-forward neural network. It needs less number of hidden nodes and testing time than ELM. In this paper, we mainly give the theoretical analysis for USUA. Theoretical results show that the error function monotonously decreases in the training procedure, the gradient of the error function with respect to weights tends to zero (the weak convergence), and the weight sequence goes to a fixed point (the strong convergence) when the iterations approach positive infinity. An illustrated simulation has been implemented on the MNIST database of handwritten digits which effectively verifies the theoretical results.
    Źródło:
    Journal of Applied Computer Science Methods; 2016, 8 No. 1; 5-15
    1689-9636
    Pojawia się w:
    Journal of Applied Computer Science Methods
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong and weak stability of some Markov operators
    Autorzy:
    Rudnicki, Ryszard
    Powiązania:
    https://bibliotekanauki.pl/articles/965771.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    biomathematics
    weak and strong convergence of measures
    Markov operators
    Opis:
    An integral Markov operator $P$ appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let $μ$ and $ν$ be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence $(P^{n}μ-P^{n}ν)$ to $0$ are given.
    Źródło:
    Colloquium Mathematicum; 2000, 84/85, 1; 255-263
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces
    Autorzy:
    Saluja, G. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255600.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    strictly asymptotically pseudo-contractive mapping
    implicit iteration scheme
    common fixed point
    strong convergence
    weak convergence
    Hilbert space
    Opis:
    In this paper, we establish the weak and strong convergence theorems for a k-strictly asymptotically pseudo-contractive mapping in the framework of Hilbert spaces. Our result improve and extend the corresponding result of Acedo and Xu, Liu, Marino and Xu, Osilike and Akuchu, and some others.
    Źródło:
    Opuscula Mathematica; 2010, 30, 4; 485-494
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong convergence theorem of a hybrid projection algorithm for a family of quasi-φ-asymptotically nonexpansive mappings
    Autorzy:
    Tang, J. F.
    Chang, S. S.
    Liu, M.
    Liu, J. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255543.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quasi-phi-asymptotically nonexpansive mapping
    asymptotically regular mapping
    hybrid projection iterative algorithm
    strong convergence theorem
    Opis:
    The main purpose of this paper is by using a new hybrid projection iterative algorithm to prove some strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The results presented in the paper improve and extend the corresponding results announced by some authors.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 341-348
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces
    Autorzy:
    Kozlowski, W.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/746461.pdf
    Data publikacji:
    2014
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    fixed point
    nonexpansive mapping
    nonexpansive semigroup
    fixed point iteration process
    implicit iterative process
    strong convergence
    uniformly convex Banach space
    Opis:
    Let \(C\) be a convex compact subset of a uniformly convex Banach space. Let \(\{T_t\}_{t \geq0}\) be a strongly-continuous nonexpansive semigroup on \(C\). Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on \(\{c_k\}\) and \(\{t_k\}\), the sequence \(\{x_k\}_{n=1}^\infty\) converges strongly to a common fixed point of the semigroup \(\{T_t\}_{t \geq0}\). There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.
    Źródło:
    Commentationes Mathematicae; 2014, 54, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators
    Autorzy:
    Saluja, G. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/952767.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    asymptotically quasi-nonexpansive in the intermediate sense random operator
    implicit random iteration process with errors
    common random fixed point
    strong convergence
    separable uniformly convex Banach space
    Opis:
    In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (C) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 327-340
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators
    Autorzy:
    Saluja, G. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/952775.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    asymptotically quasi-nonexpansive in the intermediate sense random operator
    implicit random iteration process with errors
    common random fixed point
    strong convergence
    separable uniformly convex Banach space
    Opis:
    In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (C) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 327-340
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
    Autorzy:
    Argyros, Ioannis
    Powiązania:
    https://bibliotekanauki.pl/articles/1338691.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    superlinear
    Fréchet derivative
    weak convergence
    inexact Newton method
    strong
    forcing sequence
    Banach space
    Opis:
    We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator involved. This approach showed that the upper error bounds on the distances involved are smaller compared with the corresponding ones using hypotheses on the first Fréchet derivative. However, the conditions on the forcing sequences were not given in affine invariant form. The advantages of using conditions given in affine invariant form were explained in [3], [10]. Here we reproduce all the results obtained in [3] but using affine invariant conditions.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 4; 457-465
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong law of large numbers for additive extremum estimators
    Autorzy:
    Mexia, João
    Real, Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/729890.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Kolmogorov's strong law of large numbers
    multiple regression
    almost sure convergence
    additive extremum estimators
    Opis:
    Extremum estimators are obtained by maximizing or minimizing a function of the sample and of the parameters relatively to the parameters. When the function to maximize or minimize is the sum of subfunctions each depending on one observation, the extremum estimators are additive. Maximum likelihood estimators are extremum additive whenever the observations are independent. Another instance of additive extremum estimators are the least squares estimators for multiple regressions when the usual assumptions hold. A strong law of large numbers is derived for additive extremum estimators. This law requires only the existence of first order moments and may be of interest in connection with maximum likelihood estimators, since the usual assumption that the observations are identically distributed is discarded.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2001, 21, 2; 81-88
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Fourier coefficients of some classes of functions and their applications in approximation theory
    Autorzy:
    Ibrahimov, E.J.
    Powiązania:
    https://bibliotekanauki.pl/articles/746459.pdf
    Data publikacji:
    2014
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Fourier-Gegenbauer series
    convergence
    asymptotic estimation
    Gegenbauer transform
    strong derivative and of Gegenbauer integral
    generalized shift function
    Opis:
    In the paper, the behavior of Fourier coefficients of some classes of functions on an arbitrary orthogonal system is studied. The estimates of order of convergence to zero of Fourier-Gegenbauer coefficients are found. These estimates are precise and are of terminal character. The obtained results are used in convergence of Fourier-Gegenbauer series.
    Źródło:
    Commentationes Mathematicae; 2014, 54, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    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
      Wyświetlanie 1-11 z 11

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