01084nam0 2200277 450 00002341620081127112323.020081127d1977----km-y0itaa50------baitaITBaaderrassegna storica degli studi (1786-1977)Lidia Procesi XellaBologna<<Il>> Mulinoc1977460 p.21 cmPubblicazioni del Centro di studio per la storia della storiografia filosofica52001Pubblicazioni del Centro di studio per la storia della storiografia filosofica5Baader,Franz: vonBibliografia016.121. ed.Bibliografie di filosofiaProcesai Xella,Lidia444146ITUniversità della Basilicata - B.I.A.RICAunimarc000023416Baader91402UNIBASLETTEREEXT100120081127BAS011123BAS01BAS01BOOKBASA1Polo Storico-UmanisticoFMASFondo MasiniFMas/817/597817/597B817/5972008112704Prestabile Didattica04680nam 2200757Ia 450 991043787660332120251027114103.09783642388965364238896510.1007/978-3-642-38896-5(PPN)172427452(OCoLC)858626298(MiFhGG)GVRL6WVV(CKB)2670000000533799(MiAaPQ)EBC1398811(MiFhGG)9783642388965(EXLCZ)99267000000053379920111102d2013 uy 0engurun#---uuuuatxtccrCondition the geometry of numerical algorithms /Peter Burgisser, Felipe Cucker1st ed. 2013.Berlin ;Heidelberg Springer-Verlag20131 online resource (xxxi, 554 pages) illustrationsGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,0072-7830 ;349"ISSN: 0072-7830."9783642388958 3642388957 9783642440120 3642440126 Includes bibliographical references and index.Preface -- Overture: On the Condition of Numerical Problems and the Numbers that Measure It -- I Condition in Linear Algebra (Adagio): 1 Normwise Condition of Linear Equation Solving -- 2 Probabilistic Analysis -- 3 Error Analysis of Triangular Linear Systems -- 4 Probabilistic Analysis of Rectangular Matrices -- 5 Condition Numbers and Iterative Algorithms -- Intermezzo I: Condition of Structured Data -- II Condition in Linear Optimization (Andante): 6 A Condition Number for Polyhedral Conic Systems -- 7 The Ellipsoid Method -- 8 Linear Programs and their Solution Sets -- 9 Interior-point Methods -- 10 The Linear Programming Feasibility Problem -- 11 Condition and Linear Programming Optimization -- 12 Average Analysis of the RCC Condition Number -- 13 Probabilistic Analyses of the GCC Condition Number -- Intermezzo II: The Condition of the Condition -- III Condition in Polynomial Equation Solving (Allegro con brio): 14 A Geometric Framework for Condition Numbers -- 15 Homotopy Continuation and Newton's Method -- 16 Homogeneous Polynomial Systems -- 17 Smale's 17th Problem: I -- 18 Smale's 17th Problem: II -- 19 Real Polynomial Systems -- 20 Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case 4 -- 21 Probabilistic Analysis of Conic Condition Numbers: II. The Real Case -- Appendix .This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way.   The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition.   The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.Grundlehren der mathematischen Wissenschaften ;349.Numerical analysisGeometryAlgorismesthubAnàlisi numèricathubÀlgebra linealthubConjunts convexosthubGeometria estocàsticathubAnàlisi d'error (Matemàtica)thubProgramació (Matemàtica)thubLlibres electrònicsthubNumerical analysis.Geometry.AlgorismesAnàlisi numèricaÀlgebra linealConjunts convexosGeometria estocàsticaAnàlisi d'error (Matemàtica)Programació (Matemàtica)518Bürgisser Peter1962-61484Cucker Felipe1958-320106MiAaPQMiAaPQMiAaPQBOOK9910437876603321Condition836584UNINA