# [petsc-users] -ksp_rtol problem

Matthew Knepley knepley at gmail.com
Mon Nov 11 12:23:27 CST 2013

```On Mon, Nov 11, 2013 at 12:03 PM, Qiyue Lu <qiyuelu1 at gmail.com> wrote:

> Sorry, I made a mistake in privous email.
> in my output file, the *KSP residual norm* not the rtol is 1.0e-4 at the
> 1st iteration. My question is how this residual norm calculated? Is there
> any initial guess there? thanks
>

The residual r for some approximate solution x is

r = b - Ax

The initial residual uses the initial guess, often 0.

Matt

>
>
> On Mon, Nov 11, 2013 at 11:55 AM, Qiyue Lu <qiyuelu1 at gmail.com> wrote:
>
>> Dear All:
>>
>> I am working on a linear A*x=b system.
>> When I use *-ksp_rtol 1.0e-5 *option in the command line, I am not very
>> sure how the relative tolerance is defined.
>>
>> In my understanding:
>>
>> At the beginning, r= b-A*x_i, so rtol = ||r|| / ||b|| with 2-norm has a
>> value. with the calculation, rtol gets smaller, when the rtol_new /
>> rtol_original < 1.0e-5, the calculation will stop.
>>
>> Is my understanding correct?
>>
>> If so, how to decide the rtol at the first iteration? If initial solution
>> values are all zeros, then rtol should be 1.0. In my output file, it's a
>> value related to the matrix and can be at 1.0e-4  scale. Is there any
>> initial guess solution from preconditioner used there?
>>
>> Could you help to clarify this definition? Thanks
>>
>>
>> Qiyue Lu
>>
>
>

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