Condition

Part I. Condition in Linear Algebra ()

1. Normwise Condition of Linear Equation Solving
Peter Bürgisser, Felipe Cucker

2. Probabilistic Analysis
Peter Bürgisser, Felipe Cucker

3. Error Analysis of Triangular Linear Systems
Peter Bürgisser, Felipe Cucker

4. Probabilistic Analysis of Rectangular Matrices
Peter Bürgisser, Felipe Cucker

5. Condition Numbers and Iterative Algorithms
Peter Bürgisser, Felipe Cucker

Part II. Condition in Linear Optimization ()

6. A Condition Number for Polyhedral Conic Systems
Peter Bürgisser, Felipe Cucker

7. The Ellipsoid Method
Peter Bürgisser, Felipe Cucker

8. Linear Programs and Their Solution Sets
Peter Bürgisser, Felipe Cucker

9. Interior-Point Methods
Peter Bürgisser, Felipe Cucker

10. The Linear Programming Feasibility Problem
Peter Bürgisser, Felipe Cucker

11. Condition and Linear Programming Optimization
Peter Bürgisser, Felipe Cucker

12. Average Analysis of the RCC Condition Number
Peter Bürgisser, Felipe Cucker

13. Probabilistic Analyses of the GCC Condition Number
Peter Bürgisser, Felipe Cucker

Part III. Condition in Polynomial Equation Solving ()

14. A Geometric Framework for Condition Numbers
Peter Bürgisser, Felipe Cucker

15. Homotopy Continuation and Newton’s Method
Peter Bürgisser, Felipe Cucker

16. Homogeneous Polynomial Systems
Peter Bürgisser, Felipe Cucker

17. Smale’s 17th Problem: I
Peter Bürgisser, Felipe Cucker

18. Smale’s 17th Problem: II
Peter Bürgisser, Felipe Cucker

19. Real Polynomial Systems
Peter Bürgisser, Felipe Cucker

20. Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case
Peter Bürgisser, Felipe Cucker

21. Probabilistic Analysis of Conic Condition Numbers: II. The Real Case
Peter Bürgisser, Felipe Cucker

Keywords: Mathematics, Algorithms, Mathematics of Computing, Probability Theory and Stochastic Processes, Computational Mathematics and Numerical Analysis, Computational Science and Engineering, Optimization