The Unavoidable Condition… A Report on the Book
Peter Bürgisser, Felipe Cucker: “Condition. The Geometry of Numerical Algorithms”. Grundlehren der mathematischen Wissenschaften 349, Springer 2013, 554 pp.
The average study of condition with Gaussian and non Gaussian distributions:
The first elegant response at the Smale’s 17th problem which is detailed in the book… but to have the complete story, see also in the bibliography of the book, the papers of Beltrán-Pardo of years 2007, 2008 and 2009:
Smoothed analysis of homotopy for polynomial systems:
An concise view of condition:
A pioneer of condition:
- 5.Gastinel, N.: Linear Numerical Analysis. Academic Press, San Diego (1970) Google Scholar
A first notion of condition for linear programming:
The five precursor papers for condition at the dawn of the twenty-first century:
… Without forgetting the bound of number steps of linear homotopy to get approximate zero with respect the integral of square of condition:
The existence of a homotopy path bounded by the log of condition:
The pioneer paper of smoothed analysis. last version… but the better!
- 14.Spielman, D.A., Teng, S.-H.: Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. http://arxiv.org/pdf/cs/0111050.pdf
© Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2015