Results 91 to 100 of about 1,606 (181)

The theory and application of penalized methods or Reproducing Kernel Hilbert Spaces made easy

Statistics Surveys, 2012
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - μ(t_j))^2 + λ\int_a^b [μ"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The minimization is taken over an infinite-dimensional function space, the space of all functions with square integrable second ...
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Numerical Simulation of the Kudryashov–Sinelshchikov Equation for Modeling Pressure Waves in Liquids with Gas Bubbles

Mathematics
The Kudryashov–Sinelshchikov equation (KSE) is crucial in modeling pressure waves in liquids containing gas bubbles, capturing both nonlinear wave phenomena and dispersion effects.
Gayatri Das, Bibekananda Sitha, Rajesh Kumar Mohapatra, Predrag Stanimirović, Tzung-Pei Hong   +4 more
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Representation for the reproducing kernel Hilbert space method for a nonlinear system

, 2017
We apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.
KARATAS AKGÜL, Esra, AKGÜL, Ali, KHAN, Yasir, BALEANU, Dumitru   +3 more
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REPRODUCING KERNEL HILBERT SPACE METHOD]{REPRESENTATION FOR THE REPRODUCING KERNEL HILBERT SPACE METHOD FOR A NONLINEAR SYSTEM

Hacettepe Journal of Mathematics and Statistics, 2018
Esra Karataş Akgül, Ali Akgül, Yasir Khan, Dumitru Baleanu   +3 more
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The existence of a unique solution and stability results with numerical solutions for the fractional hybrid integro-differential equations with Dirichlet boundary conditions

Boundary Value Problems
In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique.
Zahra Eidinejad, Reza Saadati, Javad Vahidi, Chenkuan Li, Tofigh Allahviranloo   +4 more
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The method of Successive Approximations for Reproducing Kernel Hilbert Spaces (1)

, 2001
A general framework for function approximation from finite data is presented based on reproducing kernel Hilbert spaces. Key results are summarised and the normal and regularised solutions are described. A potential limitation to these solutions for large data sets is the computational burden.
Dodd, T.J., Harrison, R.F.
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Expected integration approximation under general equal measure partition

Results in Applied Mathematics
In this paper, we first use an L2−discrepancy bound to give the expected uniform integration approximation for functions in the Sobolev space H1(K) equipped with a reproducing kernel.
Xiaoda Xu, Dianqi Han, Zongyou Li, Xiangqin Lin, Zhidong Qi, Lai Zhang   +5 more
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A novel numerical approach to solutions of fractional Bagley-Torvik equation fitted with a fractional integral boundary condition

Demonstratio Mathematica
In this work, we present a sophisticated operating algorithm, the reproducing kernel Hilbert space method, to investigate the approximate numerical solutions for a specific class of fractional Begley-Torvik equations (FBTE) equipped with fractional ...
Aljazzazi Mazin, Maayah Banan, Djeddi Nadir, Al-Smadi Mohammed, Momani Shaher   +4 more
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The reproducing kernel Hilbert space method for solving Troesch’s problem

, 2014
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Representation for the reproducing kernel Hilbert space method for a nonlinear system

, 2019
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