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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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Cited by 10 (0 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 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.
Inclusion Isotone Extended Interval Arithmetic  A Toolbox Update
, 1996
"... In this report we deal with the correct formulation of a special extended interval arithmetic in the context of interval Newton like methods. We first demonstrate some of the problems arising from selected older definitions. Then we investigate the basic aim, concept, and properties important for de ..."
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Cited by 6 (0 self)
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In this report we deal with the correct formulation of a special extended interval arithmetic in the context of interval Newton like methods. We first demonstrate some of the problems arising from selected older definitions. Then we investigate the basic aim, concept, and properties important for defining a correct extended interval division. Finally, we give a proper way for defining the extended interval operations needed in our special context, and we prove their inclusion isotonicity. Additionally, we give some sample applications. We conclude with two updated implementations of our extended interval operations in the toolbox environments [2] and [3].
Directed Interval Arithmetic in Mathematica: Implementation and Applications
, 1996
"... This report presents an experimental Mathematica ..."
Computer graphics, linear interpolation, and nonstandard intervals, Manuscript
, 2008
"... Abstract. This document is an assessment of the value of optimal linear interpolation enclosures and of nonstandard intervals, especially with respect to applications in computer graphics, and of the extent a future IEEE interval standard should support these. It turns out that essentially all prese ..."
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Cited by 3 (2 self)
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Abstract. This document is an assessment of the value of optimal linear interpolation enclosures and of nonstandard intervals, especially with respect to applications in computer graphics, and of the extent a future IEEE interval standard should support these. It turns out that essentially all present applications of nonstandard intervals to practical problems can be matched by similarly efficient approaches based on standard intervals only. On the other hand, a number of applications were inspired by the use of nonstandard arithmetic. This suggests the requirement of a minimal support for nonstandard intervals, allowing implementations of nonstandard interval arithmetic to be compatible with the standard, while a full support by making one of the conflicting variants required seems not appropriate.
Extended Interval Arithmetic in IEEE FloatingPoint Environment
 Interval Computations
, 1994
"... This paper describes an implementation of a general interval arithmetic extension, which comprises the following extensions of the conventional interval arithmetic: (1) extension of the set of normal intervals by improper intervals; (2) extension of the set of arithmetic operations for normal interv ..."
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Cited by 2 (1 self)
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This paper describes an implementation of a general interval arithmetic extension, which comprises the following extensions of the conventional interval arithmetic: (1) extension of the set of normal intervals by improper intervals; (2) extension of the set of arithmetic operations for normal intervals by nonstandard operations; (3) extension by infinite intervals. We give a possible realization scheme of such an universal interval arithmetic in any programming environment supporting IEEE floatingpoint arithmetic. A PASCALXSC module is reported which allows easy programming of numerical algorithms formulated in terms of conventional interval arithmetic or of any of the enlisted extended interval spaces, and provides a common base for comparison of such numerical algorithms. 1
Tawards Credible Implementation of Inner Interval Operations
 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Volume 2 Numerical Mathematics
, 1997
"... This paper briefly outlines interval arithmetic, extended by four supplementary interval operations, discuss a source of numerical errors at the implementation of floatingpoint inner interval operations and shows different ways for their suppression. The goal is to make computations involving these ..."
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Cited by 1 (1 self)
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This paper briefly outlines interval arithmetic, extended by four supplementary interval operations, discuss a source of numerical errors at the implementation of floatingpoint inner interval operations and shows different ways for their suppression. The goal is to make computations involving these operations more accurate and credible.