Qualitative computing [[electronic resource] ] : a computational journey into nonlinearity / / Françoise Chatelin

• Autore: Chaitin-Chatelin Françoise
• Pubblicazione: Singapore ; ; Hackensack, NJ, : World Scientific, c2012
• Descrizione fisica: 1 online resource (599 p.)
• Disciplina: 511.8
• Soggetto topico: Social sciences - Data processing; Qualitative research - Data processing
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Pour mes enfants, petits et grands; Preface; Contents; 7. Homotopic Deviation in Linear Algebra; 1. Introduction to Qualitative Computing; 1.1 The art of computing before the 20th century; 1.1.1 Numeracy is not ubiquitous; 1.1.2 An irrational consequence of nonlinearity; 1.1.3 Zero: Thinking the unthinkable; 1.1.4 v1-: A complex consequence of nonlinearity; 1.1.5 Infinity: Decoding divergent series; 1.2 The unending evolution of logic due to complexification; 1.2.1 Classical analysis; 1.2.2 The creative role of zero; 1.2.3 The evolutive pressure of paradoxes on logic ; 1.2.4 Hypercomplex numbers of dimension 2k, k (1843 1912)1.3 The 20th century; 1.3.1 A paradigm shift; 1.3.2 Fixing the laws of logic a priori; 1.3.3 The eclipse of the art of computing; 1.3.4 The rise of numerical linear algebra; 1.3.5 Contemporary experimental sciences; 1.4 Back to the art of computing; 1.4.1 Hypercomputation in Dickson algebras; 1.4.2 Homotopic Deviation in associative linear algebra over C; 1.4.3 Understanding why and explaining how; 1.4.4 Qualitative Computing; 2. Hypercomputation in Dickson Algebras; 2.1 Associativity in algebra; 2.1.1 Groups, rings and fields ; 2.1.2 Real algebras 2.2 Dickson algebras over the real field; 2.2.1 The doubling process of Dickson (1912); 2.2.2 "Complexification" of Ak-1: Ak = Ak-11 Ak-1D7; , k 1; 2.2.3 The k basic generators for Ak, k 2265; 1; 2.2.4 Productive coupling of linear subspaces in Ak, k 2265; 4; 2.2.5 Other inductive multiplicative processes; 2.3 Properties of the multiplication; 2.3.1 The partition Ak = R1 2295; Ak, k 2265; 1; 2.3.2 The commutator for k 2265; 2; 2.3.3 The associator for k 2265; 3; 2.3.4 The four real division algebras; 2.3.5 The alternator for k 2265; 4; 2.3.6 The normalisatrix function for k 2265; 4 ; 2.3.7 The subalgebra σx generated by x 2208; A, x 02.4 Left and right multiplication maps; 2.4.1 Definition; 2.4.2 The real scalar product La, Lb F; 2.5 The partition Ak = C1 2295; Dk, k 2265; 2; 2.5.1 A characterization of C in Ak, k 2265; 4; 2.5.2 Algebraic computation in Dk, k 2265; 2; 2.5.3 The map La for a 2208; Dk; 2.5.4 The complex scalar product La,Lb F* for a 2208; Dk; 2.6 Alternative vectors in Ak for k 2265; 4; 2.6.1 Definition; 2.6.2 Colinearity of X and Y in Ak, k 2265; 4; 2.6.3 Characterization of alternativity for vectors inAk, k 2265; 4; 2.6.4 Alternative subspaces in Ak, k 2265; 4 ; 2.9.4.3 The exponential of a product x D7; u in Ak, k 2265; 2
• Sommario/riassunto: 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
• Titolo autorizzato: Qualitative computing
• ISBN: 1-283-59365-3; 9786613906106; 981-4322-93-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910792082703321
• Lo trovi qui: Univ. Federico II