This article proposes a general and efficient filter topology reconfiguration method based on matrix completion theory, which allows for frequency-dependent couplings (FDCs) and nonresonating nodes (NRNs). The projected gradient of the objective function on the manifold of constraints is determined analytically, expressed as the stiff ordinary differential equation (ODE). This constructs the descent flow that can be numerically followed to solve the ODE with integration. Since all the gradient calculations are performed with advanced matrix operations instead of elementwise computation, the proposed synthesis algorithm is significantly efficient. Moreover, to cover more varied filter networks, the ODE expressions of the projected gradient are extended to the topologies incorporating FDCs and NRNs. Multiple synthesis examples are presented to demonstrate the efficiency of the approach. In particular, one experimental example is used to exhibit the parameter extraction application of the proposed method for post-production tuning.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.