On the stability of a modified Nyström method for Mellin convolution equations in weighted spaces

2017 ◽  
Vol 79 (2) ◽  
pp. 611-631 ◽  
Author(s):  
M. C. De Bonis ◽  
C. Laurita
Keyword(s):  
Weighted Spaces ◽  
Nyström Method ◽  
Nystrom Method ◽  
The Stability ◽  
Mellin Convolution ◽  
Convolution Equations

scholarly journals Features of the Nyström Method for the Sherman-Lauricella Equation on Piecewise Smooth Contours

2011 ◽  
Vol 1 (4) ◽  
pp. 403-414 ◽  
Author(s):  
Victor D. Didenko ◽  
Johan Heising
Keyword(s):  
Approximation Method ◽  
Toeplitz Operators ◽  
Corner Point ◽  
Opening Angle ◽  
Complicated Structure ◽  
Nyström Method ◽  
Special Model ◽  
Nystrom Method ◽  
Corner Points ◽  
The Stability

AbstractThe stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points cj, j = 0, 1, …, m relies on the invertibility of certain operators belonging to an algebra of Toeplitz operators. The operators do not depend on the shape of the contour, but on the opening angle θj of the corresponding corner cj and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle In the interval (0.1π, 1.9π), it is found that there are 8 values of θj where the invertibility of the operator may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification.

scholarly journals Numerical treatment of the generalized Love integral equation

2020 ◽  
Author(s):  
Luisa Fermo ◽  
Maria Grazia Russo ◽  
Giada Serafini
Keyword(s):  
Integral Equation ◽  
Quadrature Formula ◽  
Numerical Procedure ◽  
Quadrature Rule ◽  
Weighted Spaces ◽  
Stability And Convergence ◽  
Numerical Treatment ◽  
Nyström Method ◽  
Numerical Tests ◽  
The Stability

Abstract In this paper, the generalized Love integral equation has been considered. In order to approximate the solution, a Nyström method based on a mixed quadrature rule has been proposed. Such a rule is a combination of a product and a “dilation” quadrature formula. The stability and convergence of the described numerical procedure have been discussed in suitable weighted spaces and the efficiency of the method is shown by some numerical tests.

Predictive Nyström method for kernel methods

2017 ◽  
Vol 234 ◽  
pp. 116-125 ◽  
Author(s):  
Jiangang Wu ◽  
Lizhong Ding ◽  
Shizhong Liao
Keyword(s):  
Kernel Methods ◽  
Nyström Method ◽  
Nystrom Method

scholarly journals Matrix compression using the Nyström method

2016 ◽  
Vol 20 (5) ◽  
pp. 997-1019 ◽  
Author(s):  
Arik Nemtsov ◽  
Amir Averbuch ◽  
Alon Schclar
Keyword(s):  
Nyström Method ◽  
Nystrom Method ◽  
Matrix Compression
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