I appreciate Zu-Qing Qu for the interest shown and for making useful comments on the contents of my paper.

The reduced order matrices $MR$ and $KR$ retain the same form as given in Eq. (1) as the iterations progress. The computation results presented by Zu-Qing Qu seem to be incorrect.

With the help of the procedure in Sec. 3 of my paper, the computations for the first three iterations are carried out on the numerical example cited by Zu-Qing Qu. The results of the first three iterations are given in Table 1 hereunder.

Table
 $MR$ and $KR$ for three iterations Iteration Case 1 Case 2 $MR$ $KR$ $MR$ $KR$ 0 0 1 1 0 0 1 1 0 −1 −1 0 1 −1 0.1111 0 0.333 1 0 1 1 0 0 1 1 0 −3.0 −1 0 1 −1.481 −0.111 0 0.333 2 0 1 1 0 0 1 1 0 −3.0 −0.5165 0 1 −1.50 −0.167 0 0.333 3 0 1 1 0 0 1 1 0 −4.1111 −0.4444 0 1 −1.572 −0.161 0 0.333 10 0 1 1 0 0 1 1 0 −4.765 −0.516 0 1 −1.588 −0.172 0 0.333
 $MR$ and $KR$ for three iterations Iteration Case 1 Case 2 $MR$ $KR$ $MR$ $KR$ 0 0 1 1 0 0 1 1 0 −1 −1 0 1 −1 0.1111 0 0.333 1 0 1 1 0 0 1 1 0 −3.0 −1 0 1 −1.481 −0.111 0 0.333 2 0 1 1 0 0 1 1 0 −3.0 −0.5165 0 1 −1.50 −0.167 0 0.333 3 0 1 1 0 0 1 1 0 −4.1111 −0.4444 0 1 −1.572 −0.161 0 0.333 10 0 1 1 0 0 1 1 0 −4.765 −0.516 0 1 −1.588 −0.172 0 0.333

In addition to the above, the eigenvalues are also extracted for the full system and the two cases of master selection. The converged eigenvalues are shown in Table 2 below.

Table
 Eigenvalues Modeno. Full system Case 1 Case 2 1 −0.0542+J 0.4549 −0.0507+J 0.4553 −0.05419+J0.4549 2 −0.0542−J 0.4549 −0.0507−J 0.4553 −0.05419−j 0.4549 3 −0.3336+J 1.2374 4 −0.3336−J 1.2374 5 −0.11225+J 1.6996 6 −0.11225−J 1.6996
 Eigenvalues Modeno. Full system Case 1 Case 2 1 −0.0542+J 0.4549 −0.0507+J 0.4553 −0.05419+J0.4549 2 −0.0542−J 0.4549 −0.0507−J 0.4553 −0.05419−j 0.4549 3 −0.3336+J 1.2374 4 −0.3336−J 1.2374 5 −0.11225+J 1.6996 6 −0.11225−J 1.6996

Further to the above, I wish to add here that since the formulation in my paper finally falls into the category of unsymmetric matrices—particularly so in the case of the mass matrix in Eq. (2)—the assumption by Zu-Qing Qu that the transformation matrices [R] and [S] are the same even for a symmetric structure is not valid.