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Тезисы докладов

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The finite-dimensional approximating of an integral equation of the first kind leads to a system of linear algebraic equations (SLAE) $K varphi=f$, where $K$ is an $N*M$ matrix, $varphi $ and $f$ are vectors of the corresponding dimension. Such system can be incompatible, degenerated or ill-conditioned. In a number of problems there is an a priori information about the form or admissible values of projections of a required solution, which can be presented by a system of inequalities $$Gvarphi leq q, eqno(1)$$ where $G$ is an $L*M$ matrix and $q$ is a vector of the $L$-dimension. In the article [1] a regularizing algorithm with the calculation of the "signal-to-noise" ratios for each projection of a required solution in the space of singular value decomposition of matrix $K$ is offered. This algorithm has an essentially smaller error of a solution in comparison with algorithms of global regularization (where only one parameter of regularization varies), but does not take into account a priori limitations (1). Therefore in the report the construction of the local regularizing algorithm, which takes into account limitation (1) is stated. The variational task permitting the construction of a regularized solution to reduce to the conjugate task of square-law programming with trivial limitations on a positiveness of factors of the Lagrange is formulated. Usage of singular value decomposition of matrix $K$ essentially reduces computing expenditures in comparison with others algorithms of solving of the task of square-law programming. The carried out computing experiments have shown, that the registration even of the trivial a priori information (for example, the nonnegativity of projections of a solution) essentially reduces an error of the solution constructed by the offered local regularizing algorithm. vspace{0.5cm} 1. Voskoboinikov Yu.E., Mukhina I.N. Regularizing Algorithm of Signal and Images Restoration with Specification of local relations noise/signal // Optoelectronics, Instrumentation and Data Processing.-1999.-N4.-p.60-70.

Примечание. Тезисы докладов публикуются в авторской редакции

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