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From Julien Martin <bal...@gmail.com>
Subject Re: commons math and the finite difference method
Date Mon, 01 Jun 2009 14:32:31 GMT
thanks,
that's what I tried but I get a singular matrix exception.
I have sent you an email on your mailbox.
Julien.

2009/6/1 Luc Maisonobe <Luc.Maisonobe@free.fr>

> Julien Martin a écrit :
> > Hello,
> >
> > I am trying to put into practice the finite difference method using
> > commons math 2.0. I am in reference to the following book: "Options,
> > futures and other derivatives" by John Hull. I have attached a gif of
> > page 445 of the 6th edition of the book. Note that I assume that the
> > discretisation of the differential equation has already being achieved.
>
> Image attachements are filtered out from messages to this list, so we
> cannot see them.
>
> >
> > I am at a loss about how to NUMERICALLY resolve the system of equations
> > in section (17.31). As I will have a system of M-1 equations each having
> > three terms on the left-hand side member, it is not possible to use a
> > square matrix.
>
> I guess you are trying to solve an overdetermined linear system, i.e. a
> system A.X = B with A having M-1 rows (M > 4) and 3 columns.
>
> Such systems are solved in least square sense. Instead of finding X such
> that A.X is exactly B, we find the X value that minimizes || A.X - B ||.
> This is done by using the Q.R decomposition.
>
> Commons-math supports this decomposition. Here is a rough idea of what
> you should do:
>
>  RealMatrix a = ...;
>  RealVector b = ...;
>  RealVector x = new QRDecompositionImpl(a).getSolver().solve(b);
>
> The QRDecompositionImpl class is currently in the
> org.apache.commons.math.linear.decomposition package. We are currently
> discussing on the developers list to decide if this package should
> remain or if it should disappear and all the classes be pushed up
> directly in the linear package. If we do this, you will only need to
> update your import statement once commons-math 2.0 is officially out.
>
> Luc
>
> >
> > Can anyone please point me to the relevant parts of the commons math API
> > and give me clues as to how to numerically resolve the equation system
> > please?
> >
> > Thanks in advance,
> >
> > Julien.
> >
> >
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