The Mystery of Intervals

The Mystery of Intervals Reminiscences “Back in the Good Old Days...” column edited by George F. Corliss by Svetoslav Markov Interval functions have often been discussed in relation to Hausdorff approxima- tions [6] at Blagovest Sendov’s seminar on Approximation Theory held regularly in the Bulgarian Academy of Sciences since 1964. Numerical computations related to the best polynomial Hausdorff approximations of certain interval functions require special attention to round-off errors [2]. In 1975 Sendov, who was my PhD super- visor, gave me reprints of papers by T. Sunaga, H. Ratschek and G. Schroder ¨ on interval arithmetic and differentiation of interval functions. I was very impressed by these papers, especially by the one from Sunaga, which I enjoyed studying thoroughly [5]. It took many centuries to human mind to grasp the mystery of numbers. G. Birkhoff notes: “We should not forget that zero and negative numbers were among the last to be accepted” [1]. The primary use of negative numbers (and zero) is to make the equation A + X = B always solvable, i.e. to make the additive semigroup (R , +) of nonnegative numbers a group. The isomorphic extension (embedding) of an Abelian semigroup into a group is now a common mathematical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

The Mystery of Intervals

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1011451822404
Publisher site
See Article on Publisher Site

Abstract

Reminiscences “Back in the Good Old Days...” column edited by George F. Corliss by Svetoslav Markov Interval functions have often been discussed in relation to Hausdorff approxima- tions [6] at Blagovest Sendov’s seminar on Approximation Theory held regularly in the Bulgarian Academy of Sciences since 1964. Numerical computations related to the best polynomial Hausdorff approximations of certain interval functions require special attention to round-off errors [2]. In 1975 Sendov, who was my PhD super- visor, gave me reprints of papers by T. Sunaga, H. Ratschek and G. Schroder ¨ on interval arithmetic and differentiation of interval functions. I was very impressed by these papers, especially by the one from Sunaga, which I enjoyed studying thoroughly [5]. It took many centuries to human mind to grasp the mystery of numbers. G. Birkhoff notes: “We should not forget that zero and negative numbers were among the last to be accepted” [1]. The primary use of negative numbers (and zero) is to make the equation A + X = B always solvable, i.e. to make the additive semigroup (R , +) of nonnegative numbers a group. The isomorphic extension (embedding) of an Abelian semigroup into a group is now a common mathematical

Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

References

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