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A randomized algorithm for estimating the condition number of matrices. (English) Zbl 1299.65088

Many algorithms use singular value decomposition or Lanczos methods to find the condition number of a matrix. The author presents a linear time quasi-Monte Carlo algorithm to estimate the condition number of large matrices by the computation of eigenvalues. The efficiency of the algorithm is illustrated by some numerical results.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
15A12 Conditioning of matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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