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From Sébastien Brisard (JIRA) <>
Subject [jira] [Commented] (MATH-581) Support for iterative linear solvers
Date Tue, 12 Jul 2011 03:47:00 GMT


Sébastien Brisard commented on MATH-581:

I've had afterthoughts. I think ultimately, we will have {{AbstractRealMatrix}} inherit from
{{RealLinearOperator}}, right?
Initially, I wanted to mark the difference between a _linear operator_ and a _matrix_, so
I named {{getDomainDimension}} and {{getCodomainDimension}} the methods returning respectively
the number of columns and the number of rows of the underlying matrix. I think if we want
{{AbstractRealMatrix}} and {{RealLinearOperator}} to blend nicely, I should rename these methods
according to the naming convention of the existing {{AbstractRealMatrix}}. Otherwise, the
constructors would have different signatures!
{noformat}RealLinearOperator(dimDomain, dimCodomain){noformat}
(It would be unlogical to have the codomain appear before the domain). Since {{dimDomain ==
columnDimension}} and {{dimCodomain == rowDimension}}, this would translate into
{noformat}RealLinearOperator(columnDimension, rowDimension){noformat}
as opposed to
{noformat}AbstractRealMatrix(rowDimension, columnDimension){noformat}
which is a very dangerous inconsistency. corrects this.

> Support for iterative linear solvers
> ------------------------------------
>                 Key: MATH-581
>                 URL:
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.0, Nightly Builds
>            Reporter: Sébastien Brisard
>              Labels: iterative, linear, solver
>         Attachments: MATH-581-01.patch,,,
> Dear all,
> this issue has already been discussed on the forum. The idea is to implement the most
popular linear iterative solvers (CG, SYMMLQ, etc...) in commons-math. The beauty of these
solvers is that they do not need direct access to the coefficients of the matrix, only matrix-vector
products are necessary. This is goof, as sometimes it is inetficient to store the coefficients
of the matrix.
> So basically, before implementing the iterative solvers, we need to define an interface
slightly more general than a matrix, namely LinearOperator, with only one basic operation:
matrix-vector product.
> Here are a few interfaces and abstract classes that do that. Nothing fancy yet, I just
wanted to have you advice on the implementation before I commit some solvers.
> I thought these classes could go in a package org.apache.commons.math.linearoperator,
but really, I haven't got a clue...
> Best regards,
> Sebastien

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