References

• 1. 1)
     • C. Fröberg . (1969) Introduction to numerical analysis.
  2. 2)
     • J. Timmer , T.G. Müller , I. Swameye , O. Sandra , U. Klingmüller . Modelling the nonlinear dynamics of cellular signal transduction. Int. J. Bif. Chaos , 2053 - 2060
  3. 3)
     • H.G. Bock , P. Deuflhard , E. Hairer . (1983) Recent advances in parameter identification techniques for ordinary differential equations, Numerical treatment of inverse problems in differential and integral equations.
  4. 4)
     • H.H. von Grünberg , M. Peifer , J. Timmer , M. Kollmann . Variations in substitution rate in human and mouse genomes. Phys. Rev. Lett.
  5. 5)
     • I. Swameye , T.G. Müller , J. Timmer , O. Sandra , U. Klingmüller . Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by data-based modeling. Proc. Natl. Acad. Sci. , 1028 - 1033
  6. 6)
     • A. Törn , M. Ali , S. Viitanen . Stochastic global optimization: problem classes and solution techniques. J. Glob. Optim.
  7. 7)
     • W.H. Press , S.A. Teukolsky , W.T. Vetterling , B.P. Flannery . (1992) Numerical recipes.
  8. 8)
     • W. Horbelt , J. Timmer , M. Bünner , R. Meucci , M. Ciofini . Identifying physically properties of a CO2 laser by dynamical modeling of measured time series. Phys. Rev. E
  9. 9)
     • W. Horbelt , J. Timmer , H.U. Voss . Parameter estimation in nonlinear delayed feedback systems from noisy data. Phys. Lett. A , 513 - 521
  10. 10)
      • J.R. Banga , W.D. Seider , C.A. Floudas , P.M. Pardalos . (1996) Global optimization of chemical processes using stochastic algorithms, State of the art in global optimization.
  11. 11)
      • Bock, H.G.: `Randwertproblemmethoden zur parameteridenti fizierung in systemen nichtlinearer differentialgleichungen', 1987, PhD, Universität Bonn.
  12. 12)
      • K.R. Godfray , J.J. DiStefano , E. Walter . (1985) Identifiability of model parameters, Identification and system parameter estimation.
  13. 13)
      • H.U. Voss , M. Peifer , W. Horbelt , H. Rust , J. Timmer , G. Gousebet . (2003) Identification of chaotic systems from experimental data, Chaos and its reconstruction.
  14. 14)
      • J. Stoer . On the numerical solution of constrained least squares. SIAM J. Numer. Anal. , 282 - 411
  15. 15)
      • A.H.G. Rinnooy-Kan , G.T. Timmer . Stochastic global optimization methods. Part I: Clustering methods. Math. Prog. , 27 - 56
  16. 16)
      • Kuhn, H., Tucker, A.: `Nonlinear programming', Proc. 2nd Berkeley Symp. on Mathematical Statistics and Probabilistics, 1951, University of California Press, p. 481–492.
  17. 17)
      • J. Milstein . Fitting multiple trajectories simultaneously to a model of inducible enzyme synthesis. Math. Biosci. , 175 - 184
  18. 18)
      • Horbelt, W.: `Maximum likelihood estimation in dynamical systems', 2001, PhD, University of Freiburg, Available at http://webber.physik.uni-freiburg.de/ horbelt/diss.
  19. 19)
      • T.G. Müller , J. Timmer . Parameter identification techniques for partial differential equations. Int. J. Bif. Chaos , 2053 - 2060
  20. 20)
      • S. Schuster , M. Marhl , T. Höfer . Modelling of simple and complex calcium oscillations. Eur. J. Biochem. , 1333 - 1355
  21. 21)
      • C.T. Kelley . (1999) Iterative methods for optimization.
  22. 22)
      • E. Hairer , S.P. Nørsett , G. Wanner . (1993) Solving ordinary differential equations. I: Nonstiff problems.
  23. 23)
      • J.R. Leis , M.A. Kramer . The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations. ACM Trans. Math. Softw. , 45 - 60
  24. 24)
      • A. Griewank , D. Juedes , J. Utke . Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++. ACM Trans. Math. Softw. , 131 - 167
  25. 25)
      • R.J. Hanson , K.H. Haskell . Algorithm 587: two algorithms for the linearly constrained least squares problem. ACM Trans. Math. Softw. , 323 - 333
  26. 26)
      • M. Ali , C. Storey , A. Törn . Applications of stochastic global optimization algorithms to practical problems. J. Optim. Theory Appl. , 545 - 563
  27. 27)
      • K. Schittkowski . (2002) Numerical data fitting in dynamical systems.
  28. 28)
      • K.A. Levenberg . A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. , 164 - 168
  29. 29)
      • Z.B. Zabinsky , R.L. Smith . Pure adaptive search in global optimization. Math. Prog. , 323 - 338
  30. 30)
      • J. Timmer , H. Rust , W. Horbelt , H.U. Voss . Parameteric, nonparametric and parametric modelling of a chaotic circuit time series. Phys. Lett. A , 123 - 134
  31. 31)
      • A.W. van der Vaart . (1998) Asymptotic statistics.
  32. 32)
      • O. Richter , P. Nörtersheuser , W. Pestemer . Non-linear parameter estimation in pesticide degradation. Sci. Total Environ. , 435 - 450
  33. 33)
      • T. Lohmann , H.G. Bock , J.P. Schlöder . Numerical methods for parameter estimation and optimal experimental design in chemical reaction systems. Ind. Eng. Chem. Res. , 54 - 57
  34. 34)
      • J.R. Banga , C.G. Moles , A.A. Alonso , C.A. Floudas , P.M. Pardalos . (2003) Global optimization of bioprocesses using stochastic and hybrid methods, Frontiers in global optimization.
  35. 35)
      • C.H. Bischof , A. Carle , G.F. Corliss , A. Griewank , P. Hovland . ADIFOR: generating derivative code from Fortran programs. Sci. Program. , 11 - 29
  36. 36)
      • N. Noykova , T.G. Müller , M. Gyllenberg , J. Timmer . Quantitative analysis of anaerobic wastewater treatment processes: identifiability and parameter estimation. Biotech. Bioeng. , 89 - 103
  37. 37)
      • H.G. Bock , K. Ebert , P. Deuflhard , W. Jäger . (1981) Numerical treatment of inverse problems in chemical reaction kinetics, Modelling of chemical reaction systems.
  38. 38)
      • D. Faller , U. KlingmÄuller , J. Timmer . Simulation methods for optimal experimental design in systems biology. Simulation , 717 - 725
  39. 39)
      • D.R. Cox , D.V. Hinkley . (1979) Theoretical statistics.
  40. 40)
      • J.H. Holland . (1992) Adaption in natural and artificial systems.
  41. 41)
      • L. Ljung , T. Glad . On global identifiability for arbitrary model parameterization. Automatica , 265 - 276
  42. 42)
      • L. Denis-Vidal , G. Joly-Blanchard , C. Noiret . Some effective approaches to check the identifiability of uncontrolled nonlinear systems. Math. Comput. Simul. , 35 - 44
  43. 43)
      • K. Schittkowski . Parameter estimation in systems of nonlinear equations. Num. Math. , 129 - 142
  44. 44)
      • A. Bellen , M. Zennaro . (2003) Numerical methods for delay differential equations.
  45. 45)
      • U. Kummer , L.F. Olsen , C.J. Dixon , A.K. Green , E. Bornberg-Bauer , G. Baier . Switching from simple to complex oscillations in calcium signaling. Biophys. J. , 1188 - 1195
  46. 46)
      • A.D. Stribet , P. Rosenau , A.C. Ströder , R.J. Strasser . Parameter optimisation of fast chlorophyll fluorescence induction model. Math. Comput. Simul. , 443 - 450
  47. 47)
      • T.G. Müller , J. Timmer . Fitting parameters in partial differential equations from partially observed noisy data. Phys. D , 1 - 7
  48. 48)
      • D.W. Marquardt . An algorithm for least-squares-estimation of nonlinear problems in least squares. SIAM J. Appl. Math , 431 - 441
  49. 49)
      • J.R. Leis , M.A. Kramer . ODESSA – an ordinary differential equation solver with explicit simultaneous sensitivity analysis. ACM Trans. Math. Softw. , 61 - 67
  50. 50)
      • K.E. Brenan , S.L. Campbell , L.R. Petzold . (1989) The numerical solution of initial value problems in differential-algebraic equations.
  51. 51)
      • C. Bauer , A. Frink , R. Kreckel . Introduction to the GiNaC framework for symbolic computation within the C++ programming language. J. Symbolic Com. , 1 - 12
  52. 52)
      • J.I. Ardenghi , M.C. Maciel , A.B. Verdiell . A trust-region approach for solving a parameters estimation problem from the biotechnology area. Appl. Num. Math. , 281 - 294