Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind

2021 ◽  
pp. 113696
Author(s):  
Dušan Lj. Djukić ◽  
Rada M. Mutavdžić Djukić ◽  
Lothar Reichel ◽  
Miodrag M. Spalević
Keyword(s):  
Gauss Quadrature ◽  
Quadrature Rules ◽  
Gauss Quadrature Rules ◽  
Truncated Variants

scholarly journals Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules

2020 ◽  
Vol 146 (4) ◽  
pp. 699-728
Author(s):  
Patricia Díaz de Alba ◽  
Luisa Fermo ◽  
Giuseppe Rodriguez
Keyword(s):  
Integral Equations ◽  
Numerical Approximation ◽  
Gauss Quadrature ◽  
Upper And Lower Bounds ◽  
Stability And Convergence ◽  
Quadrature Rules ◽  
Fredholm Integral Equations ◽  
Numerical Tests ◽  
Gauss Quadrature Formula ◽  
Gauss Quadrature Rules

AbstractThis paper is concerned with the numerical approximation of Fredholm integral equations of the second kind. A Nyström method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appropriate weighted spaces. The Nyström interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nyström interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.

scholarly journals Generalized anti-Gauss quadrature rules

2015 ◽  
Vol 284 ◽  
pp. 235-243 ◽  
Author(s):  
Miroslav S. Pranić ◽  
Lothar Reichel
Keyword(s):  
Gauss Quadrature ◽  
Quadrature Rules ◽  
Gauss Quadrature Rules
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