Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms [chapter]

Roman Vershynin
Banach Spaces and their Applications in Analysis  
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -computing the size of projections of high dimensional polytopes and estimating the norms of random matrices and their inverses. 1 Recently, a prandomized polynomial time pivoting algorithm for (LP) was found by Kelner and Spielman [16] . However, their algorithm generates a walk on some other polytope related to (LP) and not on P .
more » ... ed to (LP) and not on P .
doi:10.1515/9783110918298.209 fatcat:727twkaf3bd4za5olynobolhpi