topic Preconditioned CG(RCI) initial residual computation in Intel® oneAPI Math Kernel Library

Preconditioned CG(RCI) initial residual computation

nityar — Thu, 07 May 2020 16:18:22 GMT

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

Can anybody please help on

nityar — Mon, 11 May 2020 14:55:36 GMT

Can anybody please help on this?

Hello Nitya,

Kirill_V_Intel — Sat, 16 May 2020 23:32:38 GMT

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