32 research outputs found
Higher-order reverse automatic differentiation with emphasis on the third-order
It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian ( D3f(x)⋅d ) can be calculated at a cost proportional to that of a state-of-the-art method for calculating the Hessian matrix. We do this by first presenting a simple procedure for designing high order reverse methods and applying it to deduce several methods including a reverse method that calculates D3f(x)⋅d . We have implemented this method taking into account symmetry and sparsity, and successfully calculated this derivative for functions with a million variables. These results indicate that the use of third order information in a general nonlinear solver, such as Halley–Chebyshev methods, could be a practical alternative to Newton’s method. Furthermore, high-order sensitivity information is used in methods for robust aerodynamic design. An efficient high-order differentiation tool could facilitate the use of similar methods in the design of other mechanical structures
Introduction
10.1002/9781119968962.ch1Plantwide Control: Recent Developments and Applications1-1
Plantwide Control: Recent Developments and Applications
10.1002/9781119968962Plantwide Control: Recent Developments and Applications1-47
Correction procedures for extra-column effects in dynamic column breakthrough experiments
10.1016/j.ces.2008.02.023Chemical Engineering Science63102696-2706CESC
Design and Plantwide Control of a Biodiesel Plant
10.1002/9781119968962.ch14Plantwide Control: Recent Developments and Applications293-31
Selected papers from PSE ASIA 2010
Asia-Pacific Journal of Chemical Engineering63317-31