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From Intervals to -? - Towards a General Description of Validated Uncertainty (Hardcover, 1st ed. 2023)
Loot Price: R4,029
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From Intervals to -? - Towards a General Description of Validated Uncertainty (Hardcover, 1st ed. 2023)
Series: Studies in Computational Intelligence, 1041
Expected to ship within 12 - 17 working days
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This book is about methodological aspects of uncertainty
propagation in data processing. Uncertainty propagation is an
important problem: while computer algorithms efficiently process
data related to many aspects of their lives, most of these
algorithms implicitly assume that the numbers they process are
exact. In reality, these numbers come from measurements, and
measurements are never 100% exact. Because of this, it makes no
sense to translate 61 kg into pounds and get the result-as
computers do-with 13 digit accuracy. In many cases-e.g., in
celestial mechanics-the state of a system can be described by a few
numbers: the values of the corresponding physical quantities. In
such cases, for each of these quantities, we know (at least) the
upper bound on the measurement error. This bound is either provided
by the manufacturer of the measuring instrument-or is estimated by
the user who calibrates this instrument. However, in many other
cases, the description of the system is more complex than a few
numbers: we need a function to describe a physical field (e.g.,
electromagnetic field); we need a vector in Hilbert space to
describe a quantum state; we need a pseudo-Riemannian space to
describe the physical space-time, etc. To describe and process
uncertainty in all such cases, this book proposes a general
methodology-a methodology that includes intervals as a particular
case. The book is recommended to students and researchers
interested in challenging aspects of uncertainty analysis and to
practitioners who need to handle uncertainty in such unusual
situations.
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