Rational approximations of pre-filtered transfer functions via the Lanczos algorithm
(1999) Numerical Algorithms — Vol. 20, n° 4, p. 331-342 (1999)
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- 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 {(A) over cap,(b) over cap,(c) over cap} approximating the "pre-filtered" transfer function f(s)g(s), where f(s) is given in factored form f(s) = Pi(i=1)(l)(s - z(i))/Pi(i=1)(l)(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. (1999). Rational approximations of pre-filtered transfer functions via the Lanczos algorithm. Numerical Algorithms, 20(4), 331-342. https://doi.org/10.1023/A:1019168220795 (Original work published 1999)