Matrix operators in external diffraction problems

The paper proposes a method which makes it possible to reduce problems of diffraction by thin bounded screens to the inversion of rapidly diminishing matrix operators, i.e., to algorithms which are not less effective than those for internal problems. This approach includes the expansion of the field in terms of a discrete set of cylindrical (or spherical) waves and multiple semiinversion of the initial operator. This semiinversion procedure involves the expression of the unknown cylindrical-wave scattering matrices through known plane-wave scattering matrices of internal problems, as well as the identification (with explicit inversion) of singular terms reflecting other factors of the wave-scattering process.