Rational approximations of pre-filtered transfer functions via the Lanczos algorithm.

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. [ABSTRACT FROM AUTHOR]