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The Monte Carlo method to find eigenvalues and eigenvectors

Author

Listed:
  • Ciuiu, Daniel
  • Costinescu, Cristian

Abstract

In this paper we apply the Monte Carlo method to find the eigenvalues and the eigenvectors of a k-symmetric matrix A. At first we add to the main diagonal of A a real number large enough to obtain a covariance matrix B and we take into account that the minimum sum of the squares in the principal components regression (PCR) is given by the corresponding eigenvector of the minimum eigenvalue of B.

Suggested Citation

  • Ciuiu, Daniel & Costinescu, Cristian, 2008. "The Monte Carlo method to find eigenvalues and eigenvectors," MPRA Paper 15362, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15362
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    File URL: https://mpra.ub.uni-muenchen.de/15362/1/MPRA_paper_15362.pdf
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    Citations

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    Cited by:

    1. Ciuiu, Daniel, 2008. "Pattern Classification Using Secondary Components Perceptron and Economic Applications," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 5(2), pages 51-66, June.

    More about this item

    Keywords

    Principal components regression; the Monte Carlo method; eigenvalues; eigenvectors;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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