Complexity of Bezout's theorem IV: probability of success; extensions
SIAM Journal on Numerical Analysis
Complexity and real computation
Complexity and real computation
Inversion formulas for the spherical Radon transform and the generalized cosine transform
Advances in Applied Mathematics
A numerical algorithm for zero counting, I: Complexity and accuracy
Journal of Complexity
Complexity of Bezout’s Theorem VI: Geodesics in the Condition (Number) Metric
Foundations of Computational Mathematics
Complexity of Bezout’s Theorem VII: Distance Estimates in the Condition Metric
Foundations of Computational Mathematics
On the intrinsic complexity of point finding in real singular hypersurfaces
Information Processing Letters
On the geometry of polar varieties
Applicable Algebra in Engineering, Communication and Computing
Generalized polar varieties: geometry and algorithms
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Convexity Properties of the Condition Number
SIAM Journal on Matrix Analysis and Applications
A continuation method to solve polynomial systems and its complexity
Numerische Mathematik
Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems
Foundations of Computational Mathematics
Khovanskii–Rolle Continuation for Real Solutions
Foundations of Computational Mathematics
Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces
Foundations of Computational Mathematics
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We study the average complexity of certain numerical algorithms when adapted to solving systems of multivariate polynomial equations whose coefficients belong to some fixed proper real subspace of the space of systems with complex coefficients. A particular motivation is the study of the case of systems of polynomial equations with real coefficients. Along these pages, we accept methods that compute either real or complex solutions of these input systems. This study leads to interesting problems in Integral Geometry: the question of giving estimates on the average of the normalized condition number along great circles that belong to a Schubert subvariety of the Grassmannian of great circles on a sphere. We prove that this average equals a closed formula in terms of the spherical Radon transform of the condition number along a totally geodesic submanifold of the sphere.