Degenerate Kernel Approximation

2013 ◽  
pp. 199-218
Author(s):  
Rainer Kress
Keyword(s):  
Degenerate Kernel ◽  
Kernel Approximation

scholarly journals Convergence of degenerate-kernel methods

1976 ◽  
Vol 19 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Ian H. Sloan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Integral Equations ◽  
Error Bounds ◽  
Kernel Methods ◽  
Fredholm Integral Equations ◽  
Degenerate Kernel ◽  
Kernel Approximation ◽  
Convergence Results

AbstractAdditional convergence results are given for the approximate solution in the space L2(a, b) of Fredholm integral equations of the second kind, y = f + Ky, by the degenerate-kernel methods of Sloan, Burn and Datyner. Convergence to the exact solution is provided for a class of these methods (including ‘method 2’), under suitable conditions on the kernel K, and error bounds are obtained. In every case the convergence is faster than that of the best approximate solution of the form yn = Σnan1u1, where u1, …, un are the appropriate functions used in the rank-n degenerate-kernel approximation. In addition, the error for method 2 is shown to be relatively unaffected if the integral equation has an eigenvalue near 1.

Superconvergent Nyström and degenerate kernel methods for eigenvalue problems

2011 ◽  
Vol 217 (20) ◽  
pp. 7851-7866 ◽  
Author(s):  
C. Alouch ◽  
P. Sablonnière ◽  
D. Sbibih ◽  
M. Tahrichi
Keyword(s):  
Kernel Methods ◽  
Eigenvalue Problems ◽  
Degenerate Kernel

scholarly journals Bending of an Infinite beam on a base with two parameters in the absence of a part of the base

2018 ◽  
Vol 33 ◽  
pp. 02074
Author(s):  
Maxim Aleksandrovskiy ◽  
Lidiya Zaharova
Keyword(s):  
Rapid Development ◽  
Fourier Integral ◽  
Infinite Length ◽  
Degenerate Kernel ◽  
Shift Parameter ◽  
Approximate Methods ◽  
Concentrated Force ◽  
High Rise ◽  
Two Parameters

Currently, in connection with the rapid development of high-rise construction and the improvement of joint operation of high-rise structures and bases models, the questions connected with the use of various calculation methods become topical. The rigor of analytical methods is capable of more detailed and accurate characterization of the structures behavior, which will affect the reliability of objects and can lead to a reduction in their cost. In the article, a model with two parameters is used as a computational model of the base that can effectively take into account the distributive properties of the base by varying the coefficient reflecting the shift parameter. The paper constructs the effective analytical solution of the problem of a beam of infinite length interacting with a two-parameter voided base. Using the Fourier integral equations, the original differential equation is reduced to the Fredholm integral equation of the second kind with a degenerate kernel, and all the integrals are solved analytically and explicitly, which leads to an increase in the accuracy of the computations in comparison with the approximate methods. The paper consider the solution of the problem of a beam loaded with a concentrated force applied at the point of origin with a fixed value of the length of the dip section. The paper gives the analysis of the obtained results values for various parameters of coefficient taking into account cohesion of the ground.

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