Masters Thesis - TU Delft

4.1 Deflated CG and PCG MethodsWe can now write the pseudo-code of the deflated CG method:Deflated Conjugate Gradient AlgorithmChoose ¯x 0 , set i = 0, ¯r 0 = P(b−A¯x 0 ).WHILE ¯r k ̸ =0 DOi := i+1IF i = 0 DOp 1 = ¯r 0ELSEβ i = ¯rT i−1¯r i−1¯r T i−2¯r i−2p i = ¯r i−1 +β i p i−1ENDIFα i = ¯rT i−1¯r i−1p T i PAp i¯x i = ¯x i−1 +α i p i¯r i = ¯r i−1 −α i PAp iEND WHILEx orginal = Qb+P T¯x last (4.12)We see that the algorithm is barely touched, the are only little differences between it andthe original CG algorithm.We can also make a preconditioning of the system by using an SPD precondtioner M −1 , andthen apply onto it Deflated CG method. As the result we get Deflated Preconditioned CGMethod, for which present the pseudo-code on the next page.18