Interval arithmetic distributive law Department of Biomathematics
Issue Date:
Feb-1997
Publisher:
Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
Citation:
Preprint
Series/Report no.:
1997;2
Abstract:
Generalized Interval Distributive Relation. The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus efficient solution of interval algebraic problems. All possible cases of distributivity on multiplication and addition of extended intervals are derived and presented by sharp conditional relations generalizing the distributive relations for normal intervals. A complete proof of the conditionally distributive law in its two equivalent forms, specifying how and in what case a common multiplier can be taken out of brackets or brackets can be disclosed multiplying an interval sum, is given. The impact of the generalized distributive relations on the solution of iuterval algebraic equations, symbolic manipulation and algebraic simplification of interval arithmetic expressions is outlined. AMS Subject Classification: 65G10.
