000 04429nam a22005535i 4500
001 978-3-642-38896-5
003 DE-He213
005 20140220082913.0
007 cr nn 008mamaa
008 130813s2013 gw | s |||| 0|eng d
020 _a9783642388965
_9978-3-642-38896-5
024 7 _a10.1007/978-3-642-38896-5
_2doi
050 4 _aQA76.9.A43
072 7 _aPBKS
_2bicssc
072 7 _aCOM051300
_2bisacsh
082 0 4 _a518.1
_223
100 1 _aBürgisser, Peter.
_eauthor.
245 1 0 _aCondition
_h[electronic resource] :
_bThe Geometry of Numerical Algorithms /
_cby Peter Bürgisser, Felipe Cucker.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXXXI, 554 p. 32 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v349
505 0 _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 .
520 _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.
650 0 _aMathematics.
650 0 _aComputer science.
650 0 _aComputer science
_xMathematics.
650 0 _aAlgorithms.
650 0 _aMathematical optimization.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aAlgorithms.
650 2 4 _aMathematics of Computing.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aOptimization.
700 1 _aCucker, Felipe.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642388958
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v349
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-38896-5
912 _aZDB-2-SMA
999 _c98355
_d98355