Condition : the geometry of numerical algorithms /
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...
|Series:||Grundlehren der mathematischen Wissenschaften ;
|Online Access:||Online version|
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- 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 ; 21. Probabilistic analysis of conic condition numbers: II. the real case
- Appendix .