An Appraisal of Some Methods For Computing Cauchy Principal Values of Integrals

1979 ◽  
pp. 264-287 ◽  
Author(s):  
A. van der Sluis ◽  
J. R. Zweerus
Keyword(s):  
Cauchy Principal

scholarly journals The singular terms in the fundamental matrix of crystal optics

2011 ◽  
Vol 467 (2133) ◽  
pp. 2663-2689 ◽  
Author(s):  
Peter Wagner
Keyword(s):  
Explicit Formula ◽  
Fundamental Matrix ◽  
Singular Part ◽  
Wave Surface ◽  
Crystal Optics ◽  
Cauchy Principal ◽  
Singular Terms ◽  
Negatively Curved ◽  
Principal Value ◽  
Positively Curved

We derive an explicit formula for the singular part of the fundamental matrix of crystal optics. It consists of a singularity remaining fixed at the origin x =0, of delta terms located on the positively curved parts of the wave surface, the well-known Fresnel surface and of a Cauchy principal value distribution on the negatively curved part of the wave surface.

scholarly journals An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Samir A. Ashour ◽  
Hany M. Ahmed
Keyword(s):  
Numerical Evaluation ◽  
Gaussian Quadrature ◽  
Quadrature Rules ◽  
Finite Part ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Cauchy Principal Value Integrals ◽  
Principal Value

Many algorithms that have been proposed for the numerical evaluation of Cauchy principal value integrals are numerically unstable. In this work we present some formulae to evaluate the known Gaussian quadrature rules for finite part integrals , and extend Clenshow's algorithm to evaluate these integrals in a stable way.

Evaluation of Cauchy principal value integrals of oscillatory kind

2010 ◽  
Vol 217 (6) ◽  
pp. 2390-2396 ◽  
Author(s):  
Jianbing Li ◽  
Xuesong Wang ◽  
Tao Wang
Keyword(s):  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Cauchy Principal Value Integrals ◽  
Principal Value
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