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We analyze the probability that a random m-dimensional linear subspace of R^n both intersects a regular closed convex cone C\subseteq R^n and lies within distance \alpha of an m-dimensional subspace not intersecting C (except at the origin).
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Foundations of differential geometry. Vol I
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Calculus on manifolds. A modern approach to classical theorems of advanced calculus
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Geometric measure theory
H. Federer · 1969
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Theorie der konvexen Körper
T. Bonnesen and W. Fenchel · 1974
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Differential geometry, Lie groups, and symmetric spaces
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Matrix analysis
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An introduction to differentiable manifolds and Riemannian geometry
W. M. Boothby · 1986
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The probability that a numerical analysis problem is difficult
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Log-concave and unimodal sequences in algebra, combinatorics, and geometry
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Riemannian geometry
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The kinematic formula in Riemannian homogeneous spaces
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Some perturbation theory for linear programming
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Elementary topics in differential geometry
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Integralgeometrie konvexer Körper im sphärischen Raum
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Geometric measure theory
F. Morgan · 1995
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Incorporating condition measures into the complexity theory of linear programming
J. Renegar · 1995
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Linear programming, complexity theory and elementary functional analysis
J. Renegar · 1995
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Integral geometry of spherically convex bodies
S. Glasauer · 1996
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Ill-posedness and the complexity of deciding existence of solutions to linear programs
J. R. Vera · 1996
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Introduction to geometric probability
D. A. Klain and G.-C. Rota · 1997
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Complexity theory and numerical analysis
S. Smale · 1997
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Selected topics in convex geometry
M. Moszyńska · 2001
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A new condition measure, preconditioners, and relations between different measures of conditioning for conic linear systems
M. Epelman and R. M. Freund · 2002
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A characterization of the distance to infeasibility under block-structured perturbations
J. Peña · 2003
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Condition numbers of Gaussian random matrices
Z. Chen and J. J. Dongarra · 2005
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On an extension of condition number theory to nonconic convex optimization
R. M. Freund and F. Ordóñez · 2005
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Some characterizations and properties of the “distance to ill-posedness” and the condition measure of a conic linear system
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A comprehensive introduction to differential geometry. Vol. I
M. Spivak · 1999
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Understanding the geometry of infeasible perturbations of a conic linear system
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A primal-dual symmetric relaxation for homogeneous conic systems
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The probability that a slightly perturbed numerical analysis problem is difficult
P. Bürgisser, F. Cucker, and M. Lotz · 2008
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Stochastic and integral geometry
R. Schneider and W. Weil · 2008
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A geometric analysis of Renegar’s condition number, and its interplay with conic curvature
A. Belloni and R. M. Freund · 2009
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Smoothed analysis of condition numbers
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Geometric analysis of the condition of the convex feasibility problem
D. Amelunxen · 2011
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A Coordinate-Free Condition Number for Convex Programming
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