methods is given in Fig. 4.3, where the horizontal axis denotes the number $m$ of shifted linear systems that are solved. For example, in Fig. 4.3, the computational time of the shifted COCG method at $m=200$ is about 0.76 \[sec.\], which means that it required about 0.76 \[sec.\] to solve the shifted linear systems: $\{(0.400+0.001i) I - H\}{\mbox{\boldmath $x$}}^{(1)} = {\mbox{\boldmath $e$}}_1, \{(0.401+0.001i) I - H\}{\mbox{\boldmath $x$}}^{(2)} = {\mbox{\boldmath $e$}}_1, \ldots, \{(0.599+0.001i) I - H\}{\mbox{\boldmath $x$}}^{(200)} = {\mbox{\boldmath $e$}}_1$. From Fig. 4.3 we see that as the number $m$ grows larger, the shifted QMR\_SYM method required more CPU time than the other two methods. On the other hand, the shifted QMR\_SYM($B$) method required almost the same CPU time as the shifted COCG method. This phenomena can be attributed to the computational costs of updating approximate solutions for each method since there are three facts: first, we know from Fig. 4.1 that the three methods required almost the same iterations; second, the shifted QMR\_SYM($B$) method requires almost the same computational costs as the shifted COCG method, while the shifted QMR\_SYM method tends to require more computational costs per iteration than the other two methods; third, for large $m$, updating approximate solutions 