Diffraction problems and inversion of infinite structured matrices (Q1576946)

Diffraction problems generated by the Helmholtz equation are considered that can be reduced to solving infinite systems of linear equations \(SX= F\), where the operators \(S\) satisfy an identity of the form \(AS-SB= P_1P^*_1\) where \(A\) and \(B\) are diagonal matrices and \(P_1\) and \(P_2\) have a finite number of columns. An efficient solution method is presented and applied to the case of diffraction in the planar waveguide with a cross-sectional jump, absolutely soft upper boundary, and absolutely hard lower boundary.