Optimality of the double exponential formula - functional analysis approach -

1997 ◽  
Vol 75 (3) ◽  
pp. 379-395 ◽  
Author(s):  
Masaaki Sugihara
Keyword(s):  
Functional Analysis ◽  
Analysis Approach ◽  
Double Exponential ◽  
Exponential Formula ◽  
Double Exponential Formula

scholarly journals Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

2016 ◽  
Vol 54 (10) ◽  
pp. 2048-2061 ◽  
Author(s):  
Hiroyuki Fujii ◽  
Shinpei Okawa ◽  
Yukio Yamada ◽  
Yoko Hoshi ◽  
Masao Watanabe
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Double Exponential ◽  
Exponential Formula ◽  
Double Exponential Formula

scholarly journals Computing the matrix fractional power with the double exponential formula

2021 ◽  
Vol 54 ◽  
pp. 558-580
Author(s):  
Fuminori Tatsuoka ◽  
Tomohiro Sogabe ◽  
Yuto Miyatake ◽  
Tomoya Kemmochi ◽  
Shao-Liang Zhang
Keyword(s):  
Fractional Power ◽  
Double Exponential ◽  
The Matrix ◽  
Exponential Formula ◽  
Double Exponential Formula

scholarly journals Construction of conformal maps based on the locations of singularities for improving the double exponential formula

2019 ◽  
Vol 40 (4) ◽  
pp. 2746-2776
Author(s):  
Shunki Kyoya ◽  
Ken’ichiro Tanaka
Keyword(s):  
Trapezoidal Rule ◽  
Transformation Formula ◽  
Acceleration Of Convergence ◽  
Conformal Maps ◽  
Change Of Variables ◽  
Double Exponential ◽  
De Formula ◽  
Exponential Formula ◽  
Christoffel Transformation ◽  
Double Exponential Formula

Abstract The double exponential formula, or DE formula, is a high-precision integration formula using a change of variables called a DE transformation; it has the disadvantage that it is sensitive to singularities of an integrand near the real axis. To overcome this disadvantage, Slevinsky & Olver (2015, On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. SIAM J. Sci. Comput., 37, A676–A700) attempted to improve the formula by constructing conformal maps based on the locations of singularities. Based on their ideas, we construct a new transformation formula. Our method employs special types of the Schwarz–Christoffel transformation for which we can derive the explicit form. The new transformation formula can be regarded as a generalization of DE transformations. We confirm its effectiveness by numerical experiments.

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