Methods and applications of interval analysis

By R. Moore. 1979

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Citations in the corpus

Formal Security Analysis of Neural Networks using Symbolic Intervals (2018, methodology): “[32,39], we leverage interval analysis, and our empirical results show substantial performance boosting in proving security properties of DNNs.”
Nonlinear convex and concave relaxations for the solutions of parametric ODEs (2013, methodology): “This is implemented by the factorization of f1 shown in Table I with factors vi , lower and upper bounds on each factor, v i and v U i , computed through standard interval arithmetic [33], and McCormick’s convex and concave relaxation for each factor, v i and v C i .”
Branching and bounds tighteningtechniques for non-convex MINLP (2009, background): “Reformulation is only required at the root node P 0 , while linearization is also performed at all other nodes P k .”
Interval static displacement analysis for structures with interval parameters (2002, unknown): “MATHEMATICAL BACKGROUNDS In this section, we will give a brief review on the interval analysis [9–13].”
Experimental uncertainty estimation and statistics for data having interval uncertainty. (2007, background): “Interval arithmetic (Young 1931; Dwyer 1951; Moore 1966; 1979; Goos and Hartmanis 1975; Neumaier 1990) is a special case of set arithmetic defined on intervals of the real line.”
Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients (2005, unknown): “A more extensive treatment of the recursive evaluation of Taylor coefficients may be found in [13].”
The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems?and How to Avoid Them (2013, methodology): “In interval analysis [3], [4] intervals are used instead of real numbers.”
Guaranteed estimation of the parameters of nonlinear continuous‐time models: Contributions of interval analysis (2011, methodology): “IA [11, 26, 30] provides tools to compute with vectors of intervals (more concisely, boxes) [x] = [x,x] ⊂ R.”
Interval Finite Element Analysis using Interval Factor Method (2007, background): “Moore [ 11 ] and Alefeld [1] have done the pioneering work, where they established the basic theory for the interval analysis and simply discussed the interval operations and its application.”
Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model (2013, background): “, fuzzy set theory [8], DempsterShafer theory of evidence [9]-[14], possibility the ory [15]-[18] and interval analysis [19]-[21].”