LEADER 04680nam 2200757Ia 450 001 9910437876603321 005 20251027114103.0 010 $a9783642388965 010 $a3642388965 024 7 $a10.1007/978-3-642-38896-5 035 $a(PPN)172427452 035 $a(OCoLC)858626298 035 $a(MiFhGG)GVRL6WVV 035 $a(CKB)2670000000533799 035 $a(MiAaPQ)EBC1398811 035 $a(MiFhGG)9783642388965 035 $a(EXLCZ)992670000000533799 100 $a20111102d2013 uy 0 101 0 $aeng 135 $aurun#---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aCondition $ethe geometry of numerical algorithms /$fPeter Burgisser, Felipe Cucker 205 $a1st ed. 2013. 210 $aBerlin ;$aHeidelberg $cSpringer-Verlag$d2013 215 $a1 online resource (xxxi, 554 pages) $cillustrations 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v349 300 $a"ISSN: 0072-7830." 311 08$a9783642388958 311 08$a3642388957 311 08$a9783642440120 311 08$a3642440126 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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 . 330 $aThis book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way.   The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition.   The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming. 410 0$aGrundlehren der mathematischen Wissenschaften ;$v349. 606 $aNumerical analysis 606 $aGeometry 606 $aAlgorismes$2thub 606 $aAnālisi numčrica$2thub 606 $aĀlgebra lineal$2thub 606 $aConjunts convexos$2thub 606 $aGeometria estocāstica$2thub 606 $aAnālisi d'error (Matemātica)$2thub 606 $aProgramaciķ (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aNumerical analysis. 615 0$aGeometry. 615 7$aAlgorismes 615 7$aAnālisi numčrica 615 7$aĀlgebra lineal 615 7$aConjunts convexos 615 7$aGeometria estocāstica 615 7$aAnālisi d'error (Matemātica) 615 7$aProgramaciķ (Matemātica) 676 $a518 700 $aBu?rgisser$b Peter$f1962-$061484 701 $aCucker$b Felipe$f1958-$0320106 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437876603321 996 $aCondition$9836584 997 $aUNINA