Results 1 
9 of
9
Interval Computations and IntervalRelated Statistical Techniques: Tools for Estimating Uncertainty of the Results of Data Processing and Indirect Measurements
"... In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
(Show Context)
In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on [−∆, ∆], and to use the corresponding statistical techniques. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such “interval computations” methods have been developed since the 1950s. In this chapter, we provide a brief overview of related algorithms, results, and remaining open problems.
Continued fractions from Euclid to the present day
, 2000
"... this paper to indicate how continued fractions are relevant to ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
this paper to indicate how continued fractions are relevant to
Interval Computations as an Important Part of Granular Computing: An Introduction
 in Handbook of Granular Computing, Chapter 1
, 2008
"... This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing. ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing.
unknown title
"... Interval computations and intervalrelated statistical techniques: estimating uncertainty of the results of data processing and indirect measurements ..."
Abstract
 Add to MetaCart
(Show Context)
Interval computations and intervalrelated statistical techniques: estimating uncertainty of the results of data processing and indirect measurements
Constructive Mathematics, Probability Theory, Interval Mathematics, and Fuzzy Mathematics Are Important
"... The recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations — and several related areas of study — are important, and what we can learn from the successes of these areas ’ founders and promoters. ..."
Abstract
 Add to MetaCart
(Show Context)
The recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations — and several related areas of study — are important, and what we can learn from the successes of these areas ’ founders and promoters.
Are Important
"... Recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations { and several other related areas of study { are important, and what we can learn from the successes of these areas ' founders and promoters. The end of an era. On April 1 ..."
Abstract
 Add to MetaCart
(Show Context)
Recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations { and several other related areas of study { are important, and what we can learn from the successes of these areas ' founders and promoters. The end of an era. On April 1, 2015, the interval computation community was saddened to learn that Ramon “Ray ” Moore, one of the founding fathers of interval mathematics, is no longer with us. He has always been very active. And he was special. Many researchers come up with interesting and useful results, but not too many found a new direction of mathematics, direction with hundreds of followers. What made this particular direction different? What are the main objectives of science and engineering? What was different about interval mathematics, why this particular idea became successful in many applications? To understand this success, let us recall what are the main objectives of science and engineering in general.
unknown title
"... Interval computations and intervalrelated statistical techniques: estimating uncertainty of the results of data processing and indirect measurements ..."
Abstract
 Add to MetaCart
(Show Context)
Interval computations and intervalrelated statistical techniques: estimating uncertainty of the results of data processing and indirect measurements
Snellius Versneld
, 2002
"... this article to give a number of such generalisations. In our considerations we assume that we carry out a number of steps of the Archimedean algorithm, followed by addition of a few terms of one of the series expansions in this article. During the Archimedean steps we assume that we keep track of t ..."
Abstract
 Add to MetaCart
this article to give a number of such generalisations. In our considerations we assume that we carry out a number of steps of the Archimedean algorithm, followed by addition of a few terms of one of the series expansions in this article. During the Archimedean steps we assume that we keep track of the latest values of PN ; QN as well as