Trust-region methods
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Big Omicron and big Omega and big Theta
ACM SIGACT News
Parameter Estimation Using Interval Computations
SIAM Journal on Scientific Computing
Parameter range reduction for ODE models using cumulative backward differentiation formulas
Journal of Computational and Applied Mathematics
Validated solutions of initial value problems for parametric ODEs
Applied Numerical Mathematics
Brief paper: Rigorous parameter reconstruction for differential equations with noisy data
Automatica (Journal of IFAC)
Introduction to Genetic Algorithms
Introduction to Genetic Algorithms
SIAM Journal on Scientific Computing
Telescoping strategies for improved parameter estimation of environmental simulation models
Computers & Geosciences
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This paper analyzes the effectiveness of various monotonic discretizations of an ODE in a parameter range reduction algorithm. Several properties of discretizations are given, and five classes of discretizations are defined for various step numbers s. The range reduction algorithm that employs these discretizations is described. Using both analytical results based on the prototypical model x^'=@lx, and empirical results based on two more complicated models, it is shown that one particular class of discretizations (the A1OUT class) results in the tightest bounds on the parameters. This result is shown to be attributed to a certain characteristic value, A"0, of the discretization. Accumulation of these discretizations is also defined, and its usefulness in the range reduction algorithm is described.