![]() The coefficients of numerator polynomial and the denominator polynomial in a. Van Dooren, Rational and polynomial matrix factorizations via recursive pole-zero cancellation, Linear Algebra Appl. Network Theory Questions and Answers Properties of Transfer Functions 1. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Parlett, Reduction to tridiagonal form and minimal realizations, SIAM J. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Gutknecht, A completed theory of the unsymmetric Lanczos process and related algorithms. Van Dooren, Model reduction of state-space systems via an implicitly restarted Lanczos method, Numer. Lindquist, On the partial realization problem, Linear Algebra Appl. ) We now elaborate on these steps for the general case: The general causal IIR filter (G.8) (G.9) has transfer function (G. Van Dooren, Direct block tridiagonalization of single-input singleoutput systems, Systems Control Lett. Write down the state-space representation by inspection using controller canonical form for the strictly proper transfer function. Van Dooren, A rational Lanczos algorithm for model reduction, Numer. Van Dooren, On some modifications of the Lanczos algorithm and the relation with Padé approximations, in: Mathematical Research Series 7 (Akademie Verlag, Berlin, 1996) pp. Boley, Using the block clustered nonsymmetric Lanczos algorithm to solve control problems for MIMO linear systems, in: Proc. ![]()
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