Abstract
Given a single-input single-output system {A,b,c} with strictly proper transfer function g(s), we derive a Lanczos-based method to construct a tridiagonal state-space model \(\{ \hat A,\hat b,\hat c\} \) approximating the “pre-filtered” transfer function f(s)g(s), where f(s) is given in factored form \(f(s) \doteq \Pi _{i = 1}^\ell (s - z_i )/\Pi _{i = 1}^\ell (s - p_i )\). We also show how to apply this idea to the Arnoldi process and mention a few other extensions.
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Gallivan, K., Van Dooren, P. Rational approximations of pre-filtered transfer functions via the Lanczos algorithm. Numerical Algorithms 20, 331–342 (1999). https://doi.org/10.1023/A:1019168220795
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DOI: https://doi.org/10.1023/A:1019168220795