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 ... Title of program: HOAD_MathFun Catalogue Id: AFAG_v1_0 Nature of problem General optimized higher-order automatic differentiation of mathematical functions. Complex refractive index as a case study. Versions of this program held in the CPC repository in Mendeley Data AFAG_v1_0; HOAD_MathFun; 10.1016/j.cpc.2016.04.009 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)