%AVladimir Druskin%BJournal Name: Numerical Methods for large scale problems
%D2022%I
%JJournal Name: Numerical Methods for large scale problems
%K
%MOSTI ID: 10340874
%PMedium: X
%TFinite-difference quadrature and inverse scattering
%XOne of classical tasks of the network synthesis is to construct ROMs realized via ladder networks
matching rational approximations of a targeted filter transfer function. The inverse scattering can
be also viewed in the network synthesis framework. The key is continuum interpretation of the
synthesized network in terms of the underlying medium properties, aka embedding. We describe
such an embedding via finite-difference quadrature rules (FDQR), that can be viewed as extension
of the concept of the Gaussian quadrature to finite-difference schemes. One of application of this
approach is the solution of earlier intractable large scale inverse scattering problems. We also discuss
an important open question in the FDQR related to Lotharâ€™s earlier contributions, in particular, a
possibility of finite-difference Gauss-Kronrod rules
%0Journal Article
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