2016/10/19 by Yanlin Zha, Zha, Yanlin, Mario E. Villanueva +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1610.05862
openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed arithmetic operates over interval superposition models which are parameterized by a matrix with interval components. Every point in the domain of a factorable function is then associated with a sequence of components of this matrix and the superposition, i.e. Minkowski sum, of these elements encloses the image of the function at this point. Interval superposition arithmetic has a linear runtime complexity with respect to the number of variables. Besides presenting a detailed theoretical analysis of the accuracy and convergence properties of interval superposition arithmetic, the paper illustrates its advantages compared to existing set arithmetics via numerical examples.