Deflated BiCG with an Application to Model Reduction

Algorithm 3

Deflated BiCG algorithm for multiple right-hand sides.

(1) Choose and with .

(2) Solve the first dual linear systems of (1) with the standard BiCG.

(3) Compute and using (30) and (31). Set and .

(4) for   ,   do

(5)  Solve for left and right eigenvectors. Set , .

(6)  Choose .

(7)  Solve the th system of (1) by deflated BiCG with , .

(8)  Compute and . Note that and

(9) end for