Interval arithmetic and automatic error analysis in digital computing

By R. Moore. 1963

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Citations in the corpus

Formal Security Analysis of Neural Networks using Symbolic Intervals (2018, methodology): “Interval analysis is used long before to solve non-linear equations and global optimizations and has shown great success in many application domains [18, 30, 31].”
A new interval uncertain optimization method for structures using Chebyshev surrogate models (2015, background): “In this study, the interval arithmetic [22,23], which defines the fundamental arithmetic operators, is introduced into the inner loop to evaluate the maximum and minimum values of the interval functions, as the interval arithmetic can easily obtain the bounds of a design function with interval varia”
Complete search in continuous global optimization and constraint satisfaction (2004, background): “Moore’s thesis (Moore 1962) also showed that interval methods can be used to prove the nonexistence of solutions of nonlinear systems in a box (which nowadays is used to discard boxes in a branch and bound scheme) and to reduce the region where a solution can possibly lie (which is now used to…”
Verification methods: rigorous results using floating-point arithmetic (2010, background): “of A−1b, and modified as an existence test by Moore (1977). Our exposition follows Rump (1980).”
Interval analysis: theory and applications (2000, background): “thesis [63] and therefore was mainly concentrated on bounding solutions of initial value problems for ordinary di erential equations although it contained also a whole bunch of general ideas.”