Институт вычислительной математики и математической геофизики СОРАН

Abstracts

An overdtermined system of linear algebraic equations is considered. In accordance with initial problem all the components of it's solution should be non-negative. Errors in the right-hand side and the ill-conditioned system matrix result in non-positive solution of the least-square method. Smoothing and statistical regularizations would be of no use in this case.

Let the error vector of the right-hand side be be random and have a normal distribution with a known covariance matrix. We consider deviation from the least-square solution probability a quality criterion for the obtained non-negative solution. Existence of such a solution has been prooved. Finding this solution can be reduced to finding a minimum of a quadratic form.

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