Eigenvalues and condition numbers of random matrices
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Journal of Complexity
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Condition Numbers of Gaussian Random Matrices
SIAM Journal on Matrix Analysis and Applications
Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices
SIAM Journal on Matrix Analysis and Applications
The condition number of a randomly perturbed matrix
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Smoothed analysis: an attempt to explain the behavior of algorithms in practice
Communications of the ACM - A View of Parallel Computing
Worst-Case and Smoothed Analysis of the ICP Algorithm, with an Application to the k-Means Method
SIAM Journal on Computing
Smoothed analysis of condition numbers and complexity implications for linear programming
Mathematical Programming: Series A and B
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We perform a smoothed analysis of the condition number of rectangular matrices. We prove that, asymptotically, the expected value of this condition number depends only on the elongation of the matrix and not on the center and variance of the underlying probability distribution.