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Multiplication distributivity of proper and improper intervals
 RELIABLE COMPUTING
, 2001
"... The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus efficient solution of some interval algebraic problems. In this paper we summarize and present all distributive relations, known by now, on multiplic ..."
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The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus efficient solution of some interval algebraic problems. In this paper we summarize and present all distributive relations, known by now, on multiplication and addition of generalized (proper and improper) intervals.
All about Generalized Interval Distributive Relations. I. Complete Proof of the Relations
, 2000
"... The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus e cient solution of interval algebraic problems. This paper generalizes the distributive relations, known by now, on multiplication and addition of p ..."
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Cited by 4 (1 self)
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The arithmetic on an extended set of proper and improper intervals presents algebraic completion of the conventional interval arithmetic allowing thus e cient solution of interval algebraic problems. This paper generalizes the distributive relations, known by now, on multiplication and addition of proper and improper intervals. A complete proof of the main results is presented, demonstrating an original technique based on functional notations and transition formulae between different interval structures. A variety of equivalent forms and different representations are discussed together with some examples. This paper is an extraction from [19] and will be updated permanently to include current improvements, generalizations and applications of the conditionally distributive relations. The second part of the paper is scheduled for the end of 2000 and will include several directions for the application of the generalized distributive relations.
Not seeing the roots for the branches: multivalued functions in computer algebra
 SIGSAM Bull
"... We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a ..."
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We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a cubic polynomial from the Cardano formulae, which contain fractional powers. We show that some definitions of these functions result in formulae that are correct only in the sense that they give candidates for solutions; these candidates must then be tested. Formulae that are based on singlevalued functions, in contrast, are efficient and direct. 1
Using Extended Interval Algebra in Discrete Mechanics
, 2006
"... Discrete mechanics deals with discrete mechanical systems, such as cellular automata, in which time proceeds in integer steps and the configuration space is discrete. Directly modeling discrete mechanical systems is a well known alternative to starting from a continuous setting, discretizing the m ..."
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Discrete mechanics deals with discrete mechanical systems, such as cellular automata, in which time proceeds in integer steps and the configuration space is discrete. Directly modeling discrete mechanical systems is a well known alternative to starting from a continuous setting, discretizing the model, and finally force the model to the finite alphabet of a computer. The time evolution of discrete dynamical systems, however, can be calculated exactly. In order to take into account imprecision in the input data and the need to accommodate a finite alphabet, extended interval analysis is introduced in the discrete mechanical systems formulation developed by Baez and Gilliam. It is shown how the EulerLagrange equation must be modified when working with interval input.