A new framework for H2-optimal model reduction

Figures & data

Figure 1. Cumulated execution times involved in each step of algorithm 1 for different benchmark models ($n=10$).

Figure 2. Cumulated execution times as total share of each step of Algorithm 1.

Figure 3. Illustrative Bode plot of $\mathrm{\Sigma }$ and its Model Function ${\mathrm{\Sigma }}_{\mu }$.

Figure 4. Comparison of $\mathrm{\Sigma }$, ${\mathrm{\Sigma }}_{\mu }$ and ${\mathrm{\Sigma }}_{\mu ,r}$ after ${\mathcal{H}}_2$ optimization.

Figure 5. Comparison of $\mathrm{\Sigma }$, ${\mathrm{\Sigma }}_{\mu }^2$ and ${\mathrm{\Sigma }}_{\mu ,r}^2$ after repeated ${\mathcal{H}}_2$ optimization.

Table 1. Reduction results for the gyro model using zero initialization.

	IRKA				CIRKA
$n$	$k_{{\mathcal{H}}_2}$	$n_{LU}$	$t/s$	${ϵ}_{{\mathcal{H}}_2}$	$k_{\mu }$	${\sum }^{k_{{\mathcal{H}}_2}}$	$n_{LU}$	$t/s$	${ϵ}_{{\mathcal{H}}_2}$	${\widetilde{ϵ}}_{{\mathcal{H}}_2}$
10	50	246	887	0.45	4	110	8	40	0.21	0.26
20	7	61	226	0.12	2	19	11	51	0.12	0.04
30	24	356	1281	0.05	2	37	17	83	0.05	3.32e-3

Figure 6. Reduction of the gyro model using CIRKA and IRKA ($n=30$, 9th output).

Table 2. Reduction results for the gyro model using eigs initialization.

	IRKA				CIRKA
$n$	$k_{{\mathcal{H}}_2}$	$n_{LU}$	$t/s$	${ϵ}_{{\mathcal{H}}_2}$	$k_{\mu }$	${\sum }^{k_{{\mathcal{H}}_2}}$	$n_{LU}$	$t/s$	${ϵ}_{{\mathcal{H}}_2}$	${\widetilde{ϵ}}_{{\mathcal{H}}_2}$
10	1	5	19	0.28	2	8	6	25	0.41	0.26
20	9	90	323	0.17	2	30	14	60	0.12	0.05
30	9	136	493	0.03	2	40	22	96	0.02	5.57e-3

Figure 7. Comparison of relative error and its estimation for the CDplayer model.