Stochastic perturbations and smooth condition numbers

DOI10.1016/j.jco.2010.01.003zbMath1269.15003arXiv0812.2260OpenAlexW1973143743MaRDI QIDQ964920

Diego Armentano

Publication date: 21 April 2010

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.2260

zbMATH Keywords

random matricesRiemannian manifoldseigenvalue problemscondition numberssystems of linear equationsstochastic perturbationspolynomial systems of equationseigenvector problemsfinding kernels

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Real polynomials: location of zeros (26C10) Linear equations (linear algebraic aspects) (15A06) Conditioning of matrices (15A12)

Related Items

Wilkinson's bus: weak condition numbers, with an application to singular polynomial eigenproblems ⋮ Condition of Intersecting a Projective Variety with a Varying Linear Subspace ⋮ Algebraic compressed sensing ⋮ Condition length and complexity for the solution of polynomial systems ⋮ Probabilistic analyses of condition numbers ⋮ The Polynomial Eigenvalue Problem is Well Conditioned for Random Inputs ⋮ A randomized homotopy for the Hermitian eigenpair problem

Uses Software

• mctoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast linear homotopy to find approximate zeros of polynomial systems
• Fixed points, zeros and Newton's method
• Smoothed analysis of complex conic condition numbers
• Estimates on the distribution of the condition number of singular matrices
• Average condition number for solving linear equations
• Smoothed analysis of \(\kappa(A)\)
• Note on matrices with a very ill-conditioned eigenproblem
• Estimates on the condition number of random rank-deficient matrices
• Stochastic Perturbation Theory
• On the efficiency of algorithms of analysis
• Eigenvalues and Condition Numbers of Random Matrices
• Accuracy and Stability of Numerical Algorithms
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
• Riemannian geometry