Preconditioned CG(RCI) initial residual computation

[nityar]

I am using RCI implementation of CG in MKL using dcg* API. 

Can anybody explain how the initial residual is computed in preconditioned CG version. In non preconditioned version i can confirm it is  r0 =  square sum of (AX0 - b), if X0=0, is simply square sum of initial b . For preconditioned, how do we compute the value reported in parameter dpar_[2]. 

Also, in FGMRES the initial residue is norm2, i.e square root of residue reported in CG, any reason for this inconsistency?

thanks,

-Nitya

[nityar]

Can anybody please help on this?

[Kirill_V_Intel]

Hello Nitya,

I think it should be the squared norm of the preconditioned residual: || C^{-1} r0, r0 || where r0 is the initial residual r0 = (Ax - b) and C is the preconditioner. Let me know if it happens not to be so for you (I haven't done a full check).

Best,
Kirill