  Linear systems with multiple right-hand sides arise in many applications. To
solve such systems efficiently, a new deflated block GCROT($m,k$) method is
explored in this paper by exploiting a modified block Arnoldi deflation. This
deflation strategy has been shown to have the potential to improve the original
deflation which indicates an explicit block size reduction. Incorporating this
modified block Arnoldi deflation, the new algorithm can address the possible
linear dependence at each iteration during the block Arnoldi procedure and
avoids expensive computational operations. In addition, we analyze its main
mathematical properties and prove that the deflation procedure is based on a
non-increasing behavior of the singular values of the true block residual.
Moreover, as a block version of GCROT($m,k$), the new method inherits the
property of easy operability. Finally, some numerical examples also illustrate
the effectiveness of the proposed method.

Numerical Analysis