The correction to Newton's methods of optimization

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An approach to the decrease of norm of the correction in Newton’s methods of optimization, based on the Cholesky’s factorization is presented, which is based on the integration with the technique of the choice of leading element of algorithm of linear programming as a method of solving the system of equations. We investigate the issues of increasing of the numerical stability of the Cholesky’s decomposition and the Gauss’ method of exception.

Keywords: correction, algorithm, Newton’s methods of optimization, Cholesky’s decomposition, Gauss’ method of exception, linear programming, numerical stability, integration
Citation in English: Sviridenko A.B. The correction to Newton's methods of optimization // Computer Research and Modeling, 2015, vol. 7, no. 4, pp. 835-863
Citation in English: Sviridenko A.B. The correction to Newton's methods of optimization // Computer Research and Modeling, 2015, vol. 7, no. 4, pp. 835-863
DOI: 10.20537/2076-7633-2015-7-4-835-863
According to Crossref, this article is cited by:
  • Anastasiya Borisovna Sviridenko. Direct multiplicative methods for sparse matrices. Quadratic programming. // Computer Research and Modeling. 2018. — V. 10, no. 4. — P. 407. DOI: 10.20537/2076-7633-2018-10-4-407-420
  • Anastasiya Borisovna Sviridenko, Gennadiy Anatolievich Zelenkov. Correlation and realization of quasi-Newton methods of absolute optimization. // Computer Research and Modeling. 2016. — V. 8, no. 1. — P. 55. DOI: 10.20537/2076-7633-2016-8-1-55-78
  • Anastasiya Borisovna Sviridenko. Direct multiplicative methods for sparse matrices. Newton methods. // Computer Research and Modeling. 2017. — V. 9, no. 5. — P. 679. DOI: 10.20537/2076-7633-2017-9-5-679-703
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