• 제목/요약/키워드: Reproducing kernel

검색결과 72건 처리시간 0.024초

A study on convergence and complexity of reproducing kernel collocation method

  • Hu, Hsin-Yun;Lai, Chiu-Kai;Chen, Jiun-Shyan
    • Interaction and multiscale mechanics
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    • 제2권3호
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    • pp.295-319
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    • 2009
  • In this work, we discuss a reproducing kernel collocation method (RKCM) for solving $2^{nd}$ order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

REPRODUCING KERNEL KREIN SPACES

  • Yang, Mee-Hyea
    • Journal of applied mathematics & informatics
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    • 제8권2호
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    • pp.659-668
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    • 2001
  • Let S(z) be a power series with operator coefficients such that multiplication by S(z) is an everywhere defined transformation in the square summable power series C(z). In this paper we show that there exists a reproducing kernel Krein space which is state space of extended canonical linear system with transfer function S(z). Also we characterize the reproducing kernel function of the state space of a linear system.

ON 2-INNER PRODUCT SPACES AND REPRODUCING PROPERTY

  • Sababe, Saeed Hashemi
    • Korean Journal of Mathematics
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    • 제28권4호
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    • pp.973-984
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    • 2020
  • This paper is devoted to study the reproducing property on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi variable computing, this structures play the key role in probability, mathematical finance and machine learning.

BEREZIN NUMBER INEQUALITIES VIA YOUNG INEQUALITY

  • Basaran, Hamdullah;Gurdal, Mehmet
    • 호남수학학술지
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    • 제43권3호
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    • pp.523-537
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    • 2021
  • In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.

A NUMERICAL ALGORITHM FOR SINGULAR MULTI-POINT BVPS USING THE REPRODUCING KERNEL METHOD

  • Jia, Yuntao;Lin, Yingzhen
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제21권1호
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    • pp.51-60
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    • 2014
  • In this paper, we construct a complex reproducing kernel space for singular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then, we transform the problem into an equivalent operator equation, and give a numerical algorithm to provide the approximate solution. The uniform convergence of this algorithm is proved, and complexity analysis is done. Lastly, we show the validity and feasibility of the numerical algorithm by two numerical examples.

REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS

  • Geng, Fazhan;Cui, Minggen
    • Journal of applied mathematics & informatics
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    • 제28권3_4호
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    • pp.813-821
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    • 2010
  • In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.

재생커널입자법을 이용한 체적성형공정의 해석 (Analysis of Bulk Metal Forming Process by Reproducing Kernel Particle Method)

  • 한규택
    • 한국기계가공학회지
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    • 제8권3호
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    • pp.21-26
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    • 2009
  • The finite element analysis of metal forming processes often fails because of severe mesh distortion at large deformation. As the concept of meshless methods, only nodal point data are used for modeling and solving. As the main feature of these methods, the domain of the problem is represented by a set of nodes, and a finite element mesh is unnecessary. This computational methods reduces time-consuming model generation and refinement effort. It provides a higher rate of convergence than the conventional finite element methods. The displacement shape functions are constructed by the reproducing kernel approximation that satisfies consistency conditions. In this research, A meshless method approach based on the reproducing kernel particle method (RKPM) is applied with metal forming analysis. Numerical examples are analyzed to verify the performance of meshless method for metal forming analysis.

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HRKPM을 이용한 키르히호프 판의 해석 (Kirchhoff Plate Analysis by Using Hermite Reproducing Kernel Particle Method)

  • 석병호;송태한
    • 한국공작기계학회논문집
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    • 제12권5호
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    • pp.67-72
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    • 2003
  • For the analysis of Kirchhoff plate bending problems, a new meshless method is implemented. For the satisfaction of the $C^1$ continuity condition in which the first derivative is treated an another primary variable, Hermite interpolation is enforced on standard reproducing kernel particle method. In order to impose essential boundary conditions on solving $C^1$ continuity problems, shape function modifications are adopted. Through numerical tests, the characteristics and accuracy of the HRKPM are investigated and compared with the finite element analysis. By this implementatioa it is shown that high accuracy is achieved by using HRKPM for solving Kirchhoff plate bending problems.

REPRODUCING KERNEL HILBERT SPACE BASED ON SPECIAL INTEGRABLE SEMIMARTINGALES AND STOCHASTIC INTEGRATION

  • Sababe, Saeed Hashemi;Yazdi, Maryam;Shabani, Mohammad Mehdi
    • Korean Journal of Mathematics
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    • 제29권3호
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    • pp.639-647
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    • 2021
  • In this paper, we consider the integral of a stochastic process with respect of a sequence of square integrable semimartingales. By this integrals, we construct a reproducing kernel Hilbert space and study the correspondence between this space with the concepts of arbitrage and viability in mathematical finance.

A Note on Support Vector Density Estimation with Wavelets

  • Lee, Sung-Ho
    • Journal of the Korean Data and Information Science Society
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    • 제16권2호
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    • pp.411-418
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    • 2005
  • We review support vector and wavelet density estimation. The relationship between support vector and wavelet density estimation in reproducing kernel Hilbert space (RKHS) is investigated in order to use wavelets as a variety of support vector kernels in support vector density estimation.

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