On the stability of moment-matching approximations in asymptotic waveform evaluation

Fast transient thermal analysis of Fourier and non-Fourier heat conduction

“…Solutions from AWE and also Crank-Nicolson (conventional iterative solver) agree well for all the nodes, except for nodes 6, 7, 14 and 15. This is because Padé approximation is known for producing unstable response even for stable system [15,16].…”

“…The transient response at an arbitrary node of interest, i can be approximated by a lower order polynomial fraction using Padé approximation as shown in Eq. (15) and can be further simplified to partial fractions as given by Eq. (16).…”

Coping with RC(L) interconnect design headaches

“…Although this is recognized to be a form of Padé approximation, which is prone to producing unstable models of stable systems [12,24], there have been various algorithms proposed which generate stable loworder models with excellent reliability [1,2,13,12,18]. In addition, the recent introduction of the PVL algorithm provides a means of getting stable Padé approximations, with controlled error, when a large set of dominant poles are required [8].…”

Efficient model order reduction via multi-node moment matching

“…In the limit, the maximum power of the poles in an MMM approximation of any order can be limited to two in the special case when q = I. The minimum power of the poles in an MMM approximation can also be controlled by employing moment shifting [6] as discussed in section II, allowing an even greater control of the numerical characteristics of an MMM approximation. Equation (9) can be used to determine a reduced order multiple input system with a moment shifting of sh by using …”

“…Finally, moment shifting can readily be applied in MMM and was shown in [6] to improve the accuracy of moment matching approximations by eliminating the inaccuracy effects of larger magnitude poles on the dominant poles. A reduced order system of the form in (5) can be calculated with a moment shifting of sh by using equation (9) …”