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Computer Intensive Methods in Control and Signal Processing - The Curse of Dimensionality (Paperback, Softcover reprint of the original 1st ed. 1997)
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Computer Intensive Methods in Control and Signal Processing - The Curse of Dimensionality (Paperback, Softcover reprint of the original 1st ed. 1997)
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Due to the rapid increase in readily available computing power, a
corre sponding increase in the complexity of problems being tackled
has occurred in the field of systems as a whole. A plethora of new
methods which can be used on the problems has also arisen with a
constant desire to deal with more and more difficult applications.
Unfortunately by increasing the ac curacy in models employed along
with the use of appropriate algorithms with related features, the
resultant necessary computations can often be of very high
dimension. This brings with it a whole new breed of problem which
has come to be known as "The Curse of Dimensionality" . The
expression "Curse of Dimensionality" can be in fact traced back to
Richard Bellman in the 1960's. However, it is only in the last few
years that it has taken on a widespread practical significance
although the term di mensionality does not have a unique precise
meaning and is being used in a slightly different way in the
context of algorithmic and stochastic complex ity theory or in
every day engineering. In principle the dimensionality of a problem
depends on three factors: on the engineering system (subject), on
the concrete task to be solved and on the available resources. A
system is of high dimension if it contains a lot of
elements/variables and/or the rela tionship/connection between the
elements/variables is complicated."
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