The subroutine library SLICOT provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Based on numerical linear algebra routines from BLAS and LAPACK libraries, SLICOT provides methods for the design and analysis of control systems. The basic ideas behind the library are: 1. usefulness of algorithms; 2. robustness, algorithms must either return reliable results or an error or warning indicator; 3. numerical stability and accuracy: the results are as good as can be expected when working at a given precision. If possible an estimate of the achieved accuracy should be given; 4. performance with respect to speed and memory requirements. Although important because of ever increasing complexity of control problems, this objective may never be met at cost of the two previous ones; 5. portability and reusability: the library should be independent of platforms; 6. standardisation: the library is based on rigorous programming and documentation standards; 7. benchmarking, i.e., a standardised set of examples that allows an evaluation of the performance of a method as well as the implementation with respect to correctness, accuracy, and speed. Benchmarking gives also insight in the behaviour of the method and its implementation in extreme situations, i.e., for problems where the limit of the possible accuracy is reached.

References in zbMATH (referenced in 84 articles , 1 standard article )

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  1. Benner, Peter; Penke, Carolin: Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems (2022)
  2. Fazzi, Antonio; Guglielmi, Nicola; Lubich, Christian: Finding the nearest passive or nonpassive system via Hamiltonian eigenvalue optimization (2021)
  3. Varga, Andreas: On recursive computation of coprime factorizations of rational matrices (2021)
  4. Robol, Leonardo: Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equations (2020)
  5. Benner, Peter; Mitchell, Tim: Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius (2019)
  6. Benner, P.; Heiland, J.: Exponential stability and stabilization of extended linearizations via continuous updates of Riccati-based feedback (2018)
  7. Bogomolov, Sergiy; Forets, Marcelo; Frehse, Goran; Viry, Frédéric; Podelski, Andreas; Schilling, Christian: Reach set approximation through decomposition with low-dimensional sets and high-dimensional matrices (2018)
  8. Baars, S.; Viebahn, J. P.; Mulder, T. E.; Kuehn, C.; Wubs, F. W.; Dijkstra, H. A.: Continuation of probability density functions using a generalized Lyapunov approach (2017)
  9. Bosner, Nela; Karlsson, Lars: Parallel and heterogeneous (m)-Hessenberg-triangular-triangular reduction (2017)
  10. Varga, Andreas: Solving fault diagnosis problems. Linear synthesis techniques (2017)
  11. Köhler, Martin; Saak, Jens: On BLAS level-3 implementations of common solvers for (quasi-) triangular generalized Lyapunov equations (2016)
  12. Mehrmann, Volker; Poloni, Federico: An inverse-free ADI algorithm for computing Lagrangian invariant subspaces. (2016)
  13. Oară, Cristian; Flutur, Cristian; Jungers, Marc: Squaring down with zeros cancellation in generalized systems (2016)
  14. Simoncini, V.: Computational methods for linear matrix equations (2016)
  15. Benner, Peter: Theory and numerical solution of differential and algebraic Riccati equations (2015)
  16. Kressner, Daniel; Vandereycken, Bart: Subspace methods for computing the pseudospectral abscissa and the stability radius (2014)
  17. Bosner, Nela; Bujanović, Zvonimir; Drmač, Zlatko: Efficient generalized Hessenberg form and applications (2013)
  18. Mehrmann, Volker; Poloni, Federico: Using permuted graph bases in (\mathcalH_\infty) control (2013)
  19. Bini, Dario A.; Iannazzo, Bruno; Meini, Beatrice: Numerical solution of algebraic Riccati equations. (2012)
  20. Heiland, J.; Mehrmann, V.: Distributed control of linearized Navier-Stokes equations via discretized input/output maps (2012)

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