03730nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003100118041000800149050001400157050001400171072001600185072002300201082001200224100003300236245012100269260003800390264003800428300003500466336002600501337002600527338003600553347002400589490008300613505053500696520145501231650001702686650002202703650003202725650002902757650001702786650005902803650005402862650003202916650003002948650002902978710003403007773002003041776003603061830008303097856004403180978-0-387-27650-2DE-He21320141014113429.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872765027 a10.1007/0-387-27650-52doi aeng 4aTA329-348 4aTA640-643 7aTBJ2bicssc 7aMAT0030002bisacsh04a5192231 aFriedman, George J.eauthor.10aConstraint Theoryh[electronic resource] :bMultidimensional Mathematical Model Management /cby George J. Friedman. 1aBoston, MA :bSpringer US,c2005. 1aBoston, MA :bSpringer US,c2005. aXXII, 188 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aIfsr International Series on Systems Science and Engineering,x1574-0463 ;v230 aMotivations: What is Constraint Theory and why is it important?- The Four-fold way: How to Perceive Complex Mathematical Models and Well-Posed Problems -- General Results: From Protomath to Math to Metamath -- Regular Relations: Searching for the Kernels of Constraint -- Discrete and Interval Relations: The Diminished Utility of Metamodels -- The Logical Structure of Constraint: Theory A Compact Summary -- Examples of Constraint Theory Applied to Real-World Problems -- Manager and Analyst Meet Again: Gists and Schizophrenia. aThe enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable. This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint", literally trillions of times faster than a random search, determining consistency and compatibility within seconds. This text is an invaluable reference for all engineers, mathematicians and managers concerned with modeling. "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory." --Cornelius T. Leondes, UCLA "Groundbreaking work. ... Friedman's accomplishment represents engineering at its finest. ... The credibility of the theory rests upon the formal proofs which are interspersed among the illuminating hypothetical dialog sequences between manager and analyst, which bring out distinctions that the organization must face, en route to accepting Friedman's work as essential to achieve quality control in developing and applying large models." --John N. Warfield 0aEngineering. 0aComputer science. 0aElectronic data processing. 0aEngineering mathematics.14aEngineering.24aAppl.Mathematics/Computational Methods of Engineering.24aMathematical Modeling and Industrial Mathematics.24aComputational Intelligence.24aMathematics of Computing.24aComputing Methodologies.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387234182 0aIfsr International Series on Systems Science and Engineering,x1574-0463 ;v2340uhttp://dx.doi.org/10.1007/0-387-27650-5