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FOCM
2010
111views more  FOCM 2010»
13 years 2 months ago
A Note on the Finite Variance of the Averaging Function for Polynomial System Solving
In [BP08], the average complexity of linear homotopy methods to solve polynomial equations with random initial input (in a sense to be described below) was proven to be finite, an...
Carlos Beltrán, Michael Shub
FOCM
2010
143views more  FOCM 2010»
13 years 3 months ago
Algebraic Structures of B-series
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elega...
Philippe Chartier, Ernst Hairer, Gilles Vilmart
FOCM
2010
97views more  FOCM 2010»
13 years 3 months ago
Self-Concordant Barriers for Convex Approximations of Structured Convex Sets
We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the ap...
Levent Tunçel, Arkadi Nemirovski
FOCM
2010
91views more  FOCM 2010»
13 years 3 months ago
On the Ranks and Border Ranks of Symmetric Tensors
Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We...
J. M. Landsberg, Zach Teitler
FOCM
2010
82views more  FOCM 2010»
13 years 3 months ago
Stability and Instance Optimality for Gaussian Measurements in Compressed Sensing
In compressed sensing we seek to gain information about vector x ∈ RN from d << N nonadaptive linear measurements. Candes, Donoho, Tao et. al. ( see e.g. [2, 4, 8]) propos...
P. Wojtaszczyk