Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbers

التفاصيل البيبلوغرافية
العنوان: Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbers
المؤلفون: David R. Stoutemyer
المصدر: ISSAC
بيانات النشر: ACM, 2014.
سنة النشر: 2014
مصطلحات موضوعية: Normalization (statistics), Discrete mathematics, Floating point, Arithmetic underflow, Unification, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Fuzzy logic, Monic polynomial, Gaussian rational, Polynomial long division, Mathematics
الوصف: This article describes a Mathematica package that improves simplification of general non-numeric expressions containing any mixture of Gaussian rational numbers, symbolic constants, machine and arbitrary-precision floating-point numbers, together with intervals having any mixture of such endpoints. Such generalized numbers are not automatically all converted to floats or to intervals. Expressions can be multivariate and non-polynomial. Techniques include:• Recognition and unification of approximately similar and approximately proportional factors and terms.• The option of infinity-norm normalization that is more robust than monic normalization.• The option of a unit-normal quasi-primitive normalization that uses large rational approximate common divisors of mixed number types and intervals to nicely normalize sums.• A polynomial division algorithm tolerant of terms with coefficients that are float zeros or intervals containing 0.• The ability to round or underflow negligible terms while satisfying the inclusion property of interval arithmetic.The package and a more detailed version of this article will be posted at arXiv.org.
DOI: 10.1145/2608628.2627489
URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_________::34d66a44a7e8dd7d929fbf008bfd0307
https://doi.org/10.1145/2608628.2627489
رقم الانضمام: edsair.doi...........34d66a44a7e8dd7d929fbf008bfd0307
قاعدة البيانات: OpenAIRE