01475nam 2200397 450 991015473600332120230809233627.00-19-938424-X0-19-938423-1(CKB)4340000000019096(MiAaPQ)EBC4755284(EXLCZ)99434000000001909620161215h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierTales of the quantum understanding physics' most fundamental theory /Art HobsonNew York, New York :Oxford University Press,2017.©20171 online resource (305 pages) illustrationsIncludes index.0-19-067963-8 ""Tales of the Quantum" is a discussion of the fundamental principles of quantum physics for the non-scientific reader. Hobson brings together examples that illustrate the simple and logical consistency of what otherwise is viewed as a largely unapproachable topic for anyone but physicists. The book condenses topics like force, motion, and electromagnetism"--Provided by publisher.Quantum theoryQuantum theory.530.12Hobson Art1189423MiAaPQMiAaPQMiAaPQBOOK9910154736003321Tales of the quantum2754519UNINA04678nam 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)518Burgisser Peter1962-61484Cucker Felipe1958-320106MiAaPQMiAaPQMiAaPQBOOK9910437876603321Condition836584UNINA