An approach to constructing regularized projection methods to solve illposed
problems is proposed. This approach is based on a modification of the Galerkin
discretization scheme. It has been established that such a modification leads to a
significant reduction of information expenses compared to other known methods.
The approximation properties of a fully discrete projection method
for Symm’s integral equation with a infinite smooth boundary have been investigated.
For the method, error bounds have been found in the metric of Sobolev’s spaces. The
method turns out to be more accurate compared to the fully discrete collocation method
known before.
A class of approximate methods to solve operator equations of first kind with not exactly given input data is constructed. For involved methods their optimality by the order on sets of sourcewise represented solutions is proved and the bound of informational expenses is obtained. These algorithms are numerically implemented in an efficient way. An example of application of two such algorithms is given.
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