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Automatic differentiation and its program realization

Jan Hartman, Ladislav Lukšan, Jan Zítko (2009)


Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its...

Numerical analysis for optimal shape design in elliptic boundary value problems

Zdeněk Kestřánek (1988)

Aplikace matematiky

Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed...

On fuzzy input data and the worst scenario method

Jan Chleboun (2003)

Applications of Mathematics

In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set 𝒰 a d of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by 𝒰 a d and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity....

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