TAYLOR MODELS AND OTHER VALIDATED FUNCTIONAL INCLUSION METHODS

By Kyoko Makino, Martin Berz. 2003

295 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3f409dbb8d8cda353847a6e686aae80bb30b0630

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Citations in the corpus

Deterministic global optimization of nonlinear dynamic systems (2007, methodology): “a quadrature variable x5. The reformulated singular control problem is then given by: min (t) = x5(tf) ( 25 )”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “Automatic differentiation (Berz, Bischof, Corliss and Griewank 1996, Coleman and Verma 1998, Griewank 1989, 1991, 1992, Griewank and Corliss 1991) is a now classical technique for obtaining high-quality derivatives analytically and cheaply by transforming a program for function evaluation into a pro”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “Other ways of deriving rigorous interval bounds involve exact bounding of the polynomial’s first- and second-order terms (Makino and Berz, 2003; Lin and Stadtherr, 2007b) or expressing the polynomial in Bernstein bases (Lin and Rokne, 1995).”
Validated solutions of initial value problems for parametric ODEs (2007, methodology): “Arithmetic operations with Taylor models can be done using the remainder differential algebra (RDA) described by Makino and Berz [20, 23].”
SUPPRESSION OF THE WRAPPING EFFECT BY TAYLOR MODEL- BASED VERIFIED INTEGRATORS: LONG-TERM STABILIZATION BY PRECONDITIONING (2011, background): “Thus formally, the continuous case is made equivalent to the discrete case, for which the respective property follows immediately from the respective enclosure properties of Taylor models, as described for example in [16].”
Set Propagation Techniques for Reachability Analysis (2021, unknown): “Taylor models have been originally developed by Makino and Berz [78, 79, 45].”
A Chebyshev interval method for nonlinear dynamic systems under uncertainty (2013, background): “the arithmetic operations, more detailed information can be found in the relevant references [29].”
Flow*: An Analyzer for Non-linear Hybrid Systems (2013, methodology): “Structure of FLOW* TM Integrator: The Taylor model integrator implements a guaranteed integration scheme using higher-order TMs, along the lines of previous work described in [1,2,5,6].”