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FOCM
2006
87views more  FOCM 2006»
13 years 7 months ago
Index Pairs Algorithms
We introduce some modifications and extensions of the concept od index pair in the Conley index theory. We then show how these concepts may be used to overcome some difficulties in...
Marian Mrozek
FOCM
2006
63views more  FOCM 2006»
13 years 7 months ago
On an Isospectral Lie-Poisson System and Its Lie Algebra
In this paper we analyse the matrix differential system X = [N, X2 ], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with ...
Anthony M. Bloch, Arieh Iserles
FOCM
2006
50views more  FOCM 2006»
13 years 7 months ago
Online Learning Algorithms
In this paper, we study an online learning algorithm in Reproducing Kernel Hilbert Spaces (RKHS) and general Hilbert spaces. We present a general form of the stochastic gradient m...
Steve Smale, Yuan Yao
FOCM
2007
54views more  FOCM 2007»
13 years 7 months ago
Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions
We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group. This formulation gives rise t...
Evelyne Hubert, Irina A. Kogan
FOCM
2002
97views more  FOCM 2002»
13 years 7 months ago
On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods
We consider the Riemannian geometry defined on a convex set by the Hessian of a selfconcordant barrier function, and its associated geodesic curves. These provide guidance for the...
Yu. E. Nesterov, Michael J. Todd