The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
On the extension of the complex-step derivative technique to pseudospectral algorithms
Journal of Computational Physics
Accurate numerical derivatives in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Sensitivity analysis of shape memory alloy shells
Computers and Structures
Hybrid differentiation strategies for simulation and analysis of applications in C++
ACM Transactions on Mathematical Software (TOMS)
Extensions of the first and second complex-step derivative approximations
Journal of Computational and Applied Mathematics
A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows
Journal of Computational Physics
pyMDO: An Object-Oriented Framework for Multidisciplinary Design Optimization
ACM Transactions on Mathematical Software (TOMS)
Study on the design sensitivity analysis based on complex variable in eigenvalue problem
Finite Elements in Analysis and Design
Journal of Computational Physics
Application of Lattice Boltzmann Method to sensitivity analysis via complex differentiation
Journal of Computational Physics
Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
ACM Transactions on Mathematical Software (TOMS)
Nonlinear robust performance analysis using complex-step gradient approximation
Automatica (Journal of IFAC)
On the generalization of the Complex Step Method
Journal of Computational and Applied Mathematics
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
Structural and Multidisciplinary Optimization
PDE-constrained optimization with error estimation and control
Journal of Computational Physics
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A method to approximate derivatives of real functions using complex variables which avoids the subtractive cancellation errors inherent in the classical derivative approximations is described. Numerical examples illustrating the power of the approximation are presented.