A New GMRES(𝑚) Method for Markov Chains

Table 1

Numerical results of the three algorithms for one-dimensional Markov chain with identical transition rates.

Rest	GMRES			RGMRES			GGMRES
	CPU	it	Res	CPU	it	Res	CPU	it	Res
5	0.1458	227	9.9857𝑒−7	0.2071	97	1.0240𝑒−6	0.0544	32	5.6827𝑒−6
10	0.2708	78	9.7092𝑒−7	0.1832	76	9.8590𝑒−7	0.0612	30	4.0731𝑒−6
15	0.5075	59	9.9114𝑒−7	0.1317	40	1.0653𝑒−6	0.0752	23	2.2496𝑒−6
20	0.6750	45	9.8919𝑒−7	0.1762	33	1.0609𝑒−6	0.1113	21	1.5214𝑒−6
30	0.6617	23	9.2978𝑒−7	0.1963	18	8.5427𝑒−7	0.1219	12	2.3510𝑒−6