[Scipy-tickets] [SciPy] #1306: Allow for custom inner products in CG, ...

SciPy Trac scipy-tickets@scipy....
Wed Oct 13 17:18:38 CDT 2010


#1306: Allow for custom inner products in CG,...
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 Reporter:  nicki                |       Owner:  wnbell
     Type:  enhancement          |      Status:  new   
 Priority:  normal               |   Milestone:  0.9.0 
Component:  scipy.sparse.linalg  |     Version:  0.8.0 
 Keywords:                       |  
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 Hi,

 now, here's something from a mathematician:
 Numerical algorithms that are advertised to work for symmetric/Hermetian
 matrices really rely on the fact, mostly, that the linear operator
 involved is self-adjoint with respect to the inner product in use. For
 example, all real-valued symmetric matrices fulfil

    < Ax, x > = < x, Ax >

 with any real-valued vector x. The same is true for Hermitian matrices and
 the .vdot() scalar product.

 Now, there are linear operators which *are self-adjoint, but with respect
 to a special inner product such as

    Re <.,.>

 Most (all?) of the numerical algorithms apply to these linear operators
 too, always using the respective scalar product.

 As an enhancement to CG, for example, one could allow for using a custom
 scalar product such as the one above, while having the default with
 .vdot().

 Opinions on this?

 Cheers,
 Nico

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1306>
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