matrix inversion

[Randall Mackie]

Matt,

I suspect it is my collegue who asked the earlier questions about
matrix inverses this week, although I didn't realize that until
after I sent my original message.

I also suggested he just get the LU factorizations, but he insists
he needs the actual values to embed in another larger system
he'll solve.

I suppose that with the LU factorizations, you can just do
successive solves with a vector with zeros and a 1 in the appropriate
place to generate the elements you need, no?

I've asked him for more clarification on what he needs exactly.

Thanks, Randy


Matthew Knepley wrote:
> On 9/21/07, Randall Mackie <randy at geosystem.us> wrote:
>> Matt,
>>
>> There may be very valid reasons why one would want a matrix inverse,
>> say in the context of solving optimizations where you need the
>> inverse of the covariance matrix, and you need those values to
>> embed in another system.
> 
> I do not agree. What are you going to do with the inverse that cannot be
> done with LU? Backsolves against a matrix are commonplace.
> 
>   Matt
> 
>> In this case, just getting the action of the inverse times a vector
>> is not what is needed.
>>
>> Randy
>>
>>
>> Matthew Knepley wrote:
>>> On 9/21/07, Randall Mackie <randy at geosystem.us> wrote:
>>>> I have a collegue who is considering to use PETSc for programming
>>>> his problem. He would like to know if you can get the actual
>>>> inverse of a matrix, because this inverse is embedded in another
>>>> larger system that is then solved.
>>>>
>>>> I suppose that if you solve the system directly, say with SuperLU
>>>> or MUMPS, you could get the actual inverse? I looked briefly through
>>>> the manual and documentation, but it didn't jump out at me.
>>> This makes several time this week people have asked for inverses. Never
>>> never never use the inverse. Its not stable. The storage blows up. That is
>>> why factorizations were invented. Numerical analysis courses have failed
>>> the country entirely. Just use a KSP and tell it -ksp_type preonly -pc_type lu
>>> and then you can customize the matrix type for different solvers. KSPSolve()
>>> will apply the matrix. If you want to get the action on an entire matrix, this
>>> is dense and we would have to put in the BLAS3 triangular solve calls.
>>>
>>>   Matt
>>>
>>>> Any advice here?
>>>>
>>>> Thanks, Randy
>>>>
>>>> --
>>>> Randall Mackie
>>>> GSY-USA, Inc.
>>>> PMB# 643
>>>> 2261 Market St.,
>>>> San Francisco, CA 94114-1600
>>>> Tel (415) 469-8649
>>>> Fax (415) 469-5044
>>>>
>>>> California Registered Geophysicist
>>>> License No. GP 1034
>>>>
>>>>
>>>
>> --
>> Randall Mackie
>> GSY-USA, Inc.
>> PMB# 643
>> 2261 Market St.,
>> San Francisco, CA 94114-1600
>> Tel (415) 469-8649
>> Fax (415) 469-5044
>>
>> California Registered Geophysicist
>> License No. GP 1034
>>
>>
> 
> 

-- 
Randall Mackie
GSY-USA, Inc.
PMB# 643
2261 Market St.,
San Francisco, CA 94114-1600
Tel (415) 469-8649
Fax (415) 469-5044

California Registered Geophysicist
License No. GP 1034