Regularized spectral analysis and solution of equations of first genus (Q1921700)

The author collects some results, dispersed in various publications, in much his own ones, on practically solving equations of first genus of general form in a separable Hilbert space. The results are based on the technique that joins a spectral technique with the approximation of operators by matrices and using algorithms of linear algebra for computation of spectral characteristics. Analogs of the methods of Tikhonov and Ivanov are constructed. Some estimation of errors is given. Some results on a method called the parameter correction are presented without proof. The method is to construct algorithms workable in conditions of large disturbances of certain types. Some problems of practical importance, for which the methods presented can be applied, are discussed.