Finding the most probable non-negative solution of systems of linear algebraic equations by the likelihood method

V. S. Antyufeev

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A probabilistic method for regularization is proposed. This method enables one to obtain a non-negative solution to systems of linear algebraic equations. A theorem of existence of the best possible solution is proved. A numerical example of the method application is given.

Key words: system of linear equations, non-negative regularization, probability distribution, stochastic ensemble.

UDC: 519.6

Received: 23.05.2011
Revised: 07.06.2012

 English version: Numerical Analysis and Applications, 2013, 6:3, 187–196

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