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From Sébastien Brisard (Created) (JIRA) <j...@apache.org>
Subject [jira] [Created] (MATH-771) Improve javadoc for iterative linear solvers with preconditioners
Date Fri, 23 Mar 2012 08:13:28 GMT
Improve javadoc for iterative linear solvers with preconditioners
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                 Key: MATH-771
                 URL: https://issues.apache.org/jira/browse/MATH-771
             Project: Commons Math
          Issue Type: Improvement
    Affects Versions: 3.1
            Reporter: Sébastien Brisard
            Assignee: Sébastien Brisard


Preconditioning is the replacement of the linear system {{A * x = b}} with {{A * M^(-1) *
y = b}}, followed by {{x = M^(-1) * y}}, where {{M}} approximates in some sense {{A}}. There
is no consensus in the literature as to whether {{M}} of {{M^(-1)}} should be called the preconditioner.

In {{o.a.c.m3.linear}}, the Javadoc currently states that {{M}} is the preconditioner. However,
following MATH-735, the solver must be passed {{M^(-1)}} (not {{M}}!) as a {{RealLinearOperator}}.
This makes the whole Javadoc a bit obscure. It would be logical to call preconditioning the
replacement of the initial system with {{A * M * y = b}}, where {{M}} approximates in some
sense {{A^(-1)}} and will be called the preconditioner.

Such a change will make the javadoc more readable. However, it requires careful review of
the existing Javadoc for the following classes
* {{PreconditionedIterativeLinearSolver}},
* {{ConjugateGradient}},
* {{SymmLQ}},
* {{JacobiPreconditioner}},

Also, in {{PreconditionedIterativeLinearSolver}} (and its concrete implementations), the parameter
{{minv}} in {{solve()}} should be renamed {{m}}.

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