Publication: Automatic differentiation of quadrature
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

Automatic differentiation of quadrature

- Article in a journal -
 

Author(s)
Marina Menshikova , Shaun A. Forth

Published in
Optimization Methods and Software

Year
2012

Abstract
We analyse the application of automatic differentiation (ad) to the quadrature (numerical integration) of a function integrand to determine the sensitivities of the integral to variations in the limits of integration. We derive an expression for the truncation errors of such ad-derived sensitivities and relate them to the truncation error of the original, and a closely related, function quadrature. Our results hold provided the integrand is one degree higher continuously differentiable than that sufficient for convergence of its quadrature. Numerical results validate our analysis. However, utilization of algebraic expressions for such sensitivities, instead of directly applying ad, results in an approach that proves more efficient for the tetrachoric correlation estimation example we considered using our Matlab ad framework.

AD Theory and Techniques
Hierarchical Approach

BibTeX
@ARTICLE{
         Menshikova2012Ado,
       author = "Menshikova, Marina and Forth, Shaun A.",
       title = "Automatic differentiation of quadrature",
       journal = "Optimization Methods and Software",
       volume = "27",
       number = "2",
       pages = "323--335",
       year = "2012",
       doi = "10.1080/10556788.2011.561539",
       url = "http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.561539",
       eprint = "http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.561539",
       abstract = "We analyse the application of automatic differentiation (AD) to the quadrature
         (numerical integration) of a function integrand to determine the sensitivities of the integral to
         variations in the limits of integration. We derive an expression for the truncation errors of such
         AD-derived sensitivities and relate them to the truncation error of the original, and a closely
         related, function quadrature. Our results hold provided the integrand is one degree higher
         continuously differentiable than that sufficient for convergence of its quadrature. Numerical
         results validate our analysis. However, utilization of algebraic expressions for such sensitivities,
         instead of directly applying AD, results in an approach that proves more efficient for the
         tetrachoric correlation estimation example we considered using our Matlab AD framework.",
       ad_theotech = "Hierarchical Approach"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)