Convexity Properties of the Condition Number

DOI10.1137/080718681zbMath1203.15002arXiv0806.0395OpenAlexW3100714441MaRDI QIDQ3584170

Gregorio Malajovich, Michael Shub, Jean-Pierre Dedieu, Carlos Beltran

Publication date: 19 August 2010

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.0395

zbMATH Keywords

shortest pathRiemannian geometrycondition numbergeodesicFrobenius normsingular valueshyperbolic geometrylog-convexitylinear group

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Geodesics in global differential geometry (53C22) Conditioning of matrices (15A12)

Related Items (6)

Self-convexity and curvature ⋮ On the geometry and topology of the solution variety for polynomial system solving ⋮ Complexity of path-following methods for the eigenvalue problem ⋮ A continuation method to solve polynomial systems and its complexity ⋮ Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian ⋮ Complexity of sparse polynomial solving: homotopy on toric varieties and the condition metric

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