Paper Info
Title
Optimized higher-order automatic differentiation for the Faddeeva function.
Abstract
Considerable research efforts have been directed at implementing the Faddeeva function w(z) and its derivatives with respect to z, but these did not consider the key computing issue of a possible dependence of z on some variable t. The general case is to differentiate the compound function w(z(t))=w∘z(t) with respect to t by applying the chain rule for a first order derivative, or Faà di Bruno’s formula for higher-order ones. Higher-order automatic differentiation (HOAD) is an efficient and accurate technique for derivative calculation along scientific computing codes. Although codes are available for w(z), a special symbolic HOAD is required to compute accurate higher-order derivatives for w∘z(t) in an efficient manner. A thorough evaluation is carried out considering a nontrivial case study in optics to support this assertion.
Year
DOI
Venue
2016
10.1016/j.cpc.2016.04.009
Computer Physics Communications
Keywords
Field
DocType
Functions of mathematical physics,Taylor coefficients,Automatic differentiation,Brendel–Bormann model,Complex refractive index,Higher-order dispersion parameters
Byte,Operator overloading,Mathematical optimization,Function (mathematics),Algebra,Faddeeva function,Computer science,Chain rule,Fortran,Algorithm,Automatic differentiation,Test data
Journal
Volume
ISSN
Citations 
205
0010-4655
1
PageRank 
References 
Authors
0.37
8
1
Name
Order
Citations
PageRank
Isabelle Charpentier151.56