Condition The Geometry of Numerical Algorithms /

• Κύριοι συγγραφείς: Bürgisser, Peter (Συγγραφέας), Cucker, Felipe (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Σειρά: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 349
• Θέματα: Mathematics.; Computer science > Mathematics.; Computer mathematics.; Algorithms.; Mathematical optimization.; Probabilities.; Mathematics of Computing.; Probability Theory and Stochastic Processes.; Computational Mathematics and Numerical Analysis.; Computational Science and Engineering.; Optimization.

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 shape...

Πίνακας περιεχομένων:

• 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 .