Better answers to real questions. (May 2016)

• Record Type: Journal Article
• Authors: Košta, Marek; Sturm, Thomas; Dolzmann, Andreas
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 255
• Page End: 275
• Publication Date: 2016-05
• Subjects: Existential problems -- Extended quantifier elimination -- Virtual substitution; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.07.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified variables. Implementations of extended quantifier elimination for the quadratic case via virtual substitution have been successfully applied to various problems in science and engineering. So far, the answers produced by these implementations included infinitesimal and infinite numbers, which are hard to interpret in practice. We introduce here a post-processing procedure to convert, for fixed parameters, all answers into standard real numbers. The relevance of our procedure is demonstrated by application of our implementation to various examples from the literature, where it significantly improves the quality of the results.