@inproceedings{10.1007/978-3-642-02658-4_19,
    Abstract = {This paper is concerned with the problem of computing the image of a set by a polynomial function. Such image computations constitute a crucial component in typical tools for set-based analysis of hybrid systems and embedded software with polynomial dynamics, which found applications in various engineering domains. One typical example is the computation of all states reachable from a given set in one step by a continuous dynamics described by a differential or difference equation. We propose a new algorithm for over-approximating such images based on the Bernstein expansion of polynomial functions. The images are stored using template polyhedra. Using a prototype implementation, the performance of the algorithm was demonstrated on two practical systems as well as a number of randomly generated examples.},
    Address = {Berlin, Heidelberg},
    Author = {Dang, Thao and Salinas, David},
    BookTitle = {Computer Aided Verification},
    Editor = {Bouajjani, Ahmed and Maler, Oded},
    File = {Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion - Dang-Salinas2009\_Chapter\_ImageComputationForPolynomialD - a - l.pdf},
    ISBN = {978-3-642-02658-4},
    Pages = {219--232},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion},
    Year = {2009},
    date-added = {2021-01-20 19:05:47 +0100},
    date-modified = {2021-01-20 19:05:47 +0100},
    doi = {10.1007/978-3-642-02658-4_19}
}

@inproceedings{10.1007/978-3-642-02658-4_19, Abstract = {This paper is concerned with the problem of computing the image of a set by a polynomial function. Such image computations constitute a crucial component in typical tools for set-based analysis of hybrid systems and embedded software with polynomial dynamics, which found applications in various engineering domains. One typical example is the computation of all states reachable from a given set in one step by a continuous dynamics described by a differential or difference equation. We propose a new algorithm for over-approximating such images based on the Bernstein expansion of polynomial functions. The images are stored using template polyhedra. Using a prototype implementation, the performance of the algorithm was demonstrated on two practical systems as well as a number of randomly generated examples.}, Address = {Berlin, Heidelberg}, Author = {Dang, Thao and Salinas, David}, BookTitle = {Computer Aided Verification}, Editor = {Bouajjani, Ahmed and Maler, Oded}, File = {Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion - Dang-Salinas2009_Chapter_ImageComputationForPolynomialD - a - l.pdf}, ISBN = {978-3-642-02658-4}, Pages = {219--232}, Publisher = {Springer Berlin Heidelberg}, Title = {Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion}, Year = {2009}, date-added = {2021-01-20 19:05:47 +0100}, date-modified = {2021-01-20 19:05:47 +0100}, doi = {10.1007/978-3-642-02658-4_19} }