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 "e;The Curse of Dimensionality"e; . The expression "e;Curse of Dimensionality"e; 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.

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 "e;The Curse of Dimensionality"e; . The expression "e;Curse of Dimensionality"e; 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.