Basic Mathematical Definition
For a multivariate function, functional decomposition generally refers to a process of identifying a set of functions such that
where is some other function. Thus, we would say that the function is decomposed into functions . This process is intrinsically hierarchical in the sense that we can (and often do) seek to further decompose the functions into a collection of constituent functions such that
where is some other function. Decompositions of this kind are interesting and important for a wide variety of reasons. In general, functional decompositions are worthwhile when there is a certain "sparseness" in the dependency structure; that is, when constituent functions are found to depend on approximately disjoint sets of variables. Thus, for example, if we can obtain a decomposition of into a hierarchical composition of functions such that, as shown in the figure at right, this would probably be considered a highly valuable decomposition.
Read more about this topic: Functional Decomposition
Famous quotes containing the words basic, mathematical and/or definition:
“The basic rule of human nature is that powerful people speak slowly and subservient people quickly—because if they don’t speak fast nobody will listen to them.”
—Michael Caine [Maurice Joseph Micklewhite] (b. 1933)
“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
—Roger Bacon (c. 1214–c. 1294)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)