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Qualitative Computing
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A Computational Journey Into Nonlinearity
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Artikel-Nr:
9789814322928
Veröffentl:
2012
Einband:
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Erscheinungsdatum:
15.06.2012
Seiten:
600
Autor:
Francoise Chatelin
Gewicht:
1010 g
Format:
235x157x36 mm
Sprache:
Englisch
Beschreibung:
High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which expresses the creative potential of the complex plane.
Introduction to Qualitative Computing; Hypercomputation in Dickson Algebras; Scales of Complexity and Linear Reachability; Singular Values for the Multiplication Maps; Computation Beyond Classical Logic; Complexification of the Arithmetic; Homotopic Deviation in Linear Algebra; The Discrete and the Continuous; Arithmetic in the Alternative Dickson Division Algebras; The Real and the Complex.