Eigenvalues and condition numbers of random matrices
SIAM Journal on Matrix Analysis and Applications
Condition numbers of random matrices
Journal of Complexity
Applied numerical linear algebra
Applied numerical linear algebra
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
SIAM Journal on Matrix Analysis and Applications
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices
SIAM Journal on Matrix Analysis and Applications
The smoothed analysis of algorithms
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Smoothed analysis: an attempt to explain the behavior of algorithms in practice
Communications of the ACM - A View of Parallel Computing
Stochastic perturbations and smooth condition numbers
Journal of Complexity
Randomized preconditioning of the MBA algorithm
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Smoothed Analysis of Moore-Penrose Inversion
SIAM Journal on Matrix Analysis and Applications
The smoothed analysis of algorithms
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A derivative-free approximate gradient sampling algorithm for finite minimax problems
Computational Optimization and Applications
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Let A = ((aij)) be an m × m (m ≥ 3) real random matrix, with independent Gaussian entries with a common variance σ2. Denote by M the matrix of expected values of the entries of A. For x 0 we prove that P(κ(A)m.x x;(1/4√2πm + C(M, σ, m)) with C(M, σ, m) = 7(5+4||M||2(1+logm)/σ2m)1/2 Here κ(A) = ||A|| ||A-1|| is the usual condition number of A, ||.|| is Euclidean operator norm. This implies that if 0 M|| ≥ 1 then, for x 0, P(κ(A) m.x) K/σx where K is a universal constant.