The complex-step derivative approximation
نویسندگان
چکیده
منابع مشابه
The Connection between the Complex-step Derivative Approximation and Algorithmic Differentiation
This paper presents improvements to the complexstep derivative approximation method which increase its accuracy and robustness. These improvements unveil the connection to algorithmic differentiation theory. The choice between these two methods then hinges on a trade-off between ease of implementation and execution efficiency. Automatic implementations for Fortran and C/C++ are presented and th...
متن کاملNonlinear robust performance analysis using complex-step gradient approximation
In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The met...
متن کاملComplex-step Gradient Approximation for Robustness Analysis of Nonlinear Systems
In this paper, the complex-step perturbation method is extended to the setting of optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtraction cancellation error, and therefore the truncation error can be made arbitrarily small. The method is applied to t...
متن کاملTaylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization
In order to achieve higher computational precision in approximating the first-order derivative and discretize more effectively the continuous-time Zhang neural network (ZNN), a Taylor-type numerical differentiation rule is proposed and investigated in this paper. This rule not only greatly remedies some intrinsic weaknesses of the backward and central numerical differentiation rules, but also o...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Transactions on Mathematical Software
سال: 2003
ISSN: 0098-3500,1557-7295
DOI: 10.1145/838250.838251