# A simple numerical method based simultaneous stochastic perturbation for estimation of high dimensional matrices

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## Abstract

We describe a simple algorithm for estimating the elements of a matrix as well as its decomposition under the condition that only the product of this matrix with a vector is accessible. The algorithm is based on application of the stochastic simultaneous perturbation method. Theoretical results on the convergence of the proposed algorithm are proven. Numerical experiments are presented to show the efficiency of the proposed algorithm.

## Keywords

Numerical differentiation Stochastic simultaneous perturbation Matrix decomposition Singular value decomposition Parameter estimation Data assimilation## Notes

### Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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