26,574 research outputs found

    Reconstructing Rational Functions with FireFly\texttt{FireFly}

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    We present the open-source C++\texttt{C++} library FireFly\texttt{FireFly} for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use FireFly\texttt{FireFly} in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program Kira\texttt{Kira}.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio

    A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems

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    In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. Second, to analyze and compare the main computational ingredients of these algorithms, to detect their strong points and their potential bottlenecks. And finally, to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance

    Computational linear algebra over finite fields

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    We present here algorithms for efficient computation of linear algebra problems over finite fields
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