Constraint Theory: Multidimensional Mathematical Model - download pdf or read online

By George Friedman

ISBN-10: 0387234187

ISBN-13: 9780387234182

The large strength of electronic computation to control new complicated platforms is impeded via exponential raises in complexity. because the model's dimensionality raises from enormous quantities to millions of variables, and as submodels built through various technical groups are built-in into the entire version, the version is probably going to develop into inconsistent or even much more likely, the computational requests at the version turn into unallowable. this article analyzes the way in which constraint thought employs bipartite graphs and constraint matrices to realize and proper those well-posed difficulties. It additionally provides the method of finding the "kernel of constraint", actually trillions of instances speedier than a random seek, settling on consistency and compatibility inside of seconds. this article is a useful connection with all engineers, mathematicians and bosses involved in modeling.

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Additional info for Constraint Theory: Multidimensional Mathematical Model Management (IFSR International Series on Systems Science and Engineering)

Example text

Motivations 17 computational requests made on the 6-dimensional model, less than 15% were allowable. Of the 1078 computational requests made on the 8dimensional model, less than 6% were allowable. As the dimensionality of the model increases to dozens or hundreds of variables to address modern complex systems, then we can expect the allowability likelihood to diminish even further. ” “For example, let’s examine the three relations, 2, 3 and 4, that caused the inadvertent source of intrinsic constraint.

What do we really know about ‘reality,’” asked the analyst, launching into a minor tirade. “Irrational numbers were once thought to be irrational, and still bear the label. Negative numbers were once thought to be imaginary, but now play an essential role in every walk of science and finance. Zero was originally thought to be completely unworthy of serious consideration, but we would be crippled if we stuck to the awkward Roman 44 Constraint theory numerals. Imaginary numbers were originally considered as only interesting abstractions, but today form the basis of several very practical integral transforms and are essential to almost every walk of electrical engineering.

Changing K1 from a constant to a variable permits C, D, S, and K1 to act as independent variables in computations. 1. Motivations 19 Figure 1-12. A sequential computational flow in a model about S times larger than the example. “Is there a name to this process? How difficult would it be to become proficient in this technique? ” asked the manager. “The name of the process is ‘Constraint Theory’. It is based on the author’s PhD dissertation [2] and subsequent published papers [3]. The only mathematical prerequisites are the simplest 5% of set theory and graph theory.

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Constraint Theory: Multidimensional Mathematical Model Management (IFSR International Series on Systems Science and Engineering) by George Friedman


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