Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and blocktridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistorcapacitorinductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to socalled nitedierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM statespace representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from themore »
Finitedifference quadrature and inverse scattering
One 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 finitedifference quadrature rules (FDQR), that can be viewed as extension
of the concept of the Gaussian quadrature to finitedifference 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 Lothar’s earlier contributions, in particular, a
possibility of finitedifference GaussKronrod rules
 Award ID(s):
 2110773
 Publication Date:
 NSFPAR ID:
 10340874
 Journal Name:
 Numerical Methods for large scale problems
 Sponsoring Org:
 National Science Foundation
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