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Before implementing something be sure to research the subject
thoroughly. This will save a lot of time in the longrun. The two most
important steps are,

to determine whether there is already a free library (GPL or
GPLcompatible) which does the job. If so, there is no need to
reimplement it. Carry out a search on Netlib, GAMs, nanet,
sci.math.numanalysis and the web in general. This should also provide a
list of existing proprietary libraries which are relevant.

make a comparative survey of existing implementations in the
commercial/free libraries. Examine the typical APIs, methods of
communication between program and subroutine, and classify them so that
you are familiar with the key concepts or features that an
implementation may or may not have, depending on the relevant tradeoffs
chosen. Be sure to review the documentation of existing libraries for
useful references.

read up on the subject and determine the stateoftheart. Find the
latest review papers. A search of the following journals should be
undertaken.
 ACM Transactions on Mathematical Software
 Numerische Mathematik
 Journal of Computation and Applied Mathematics
 Computer Physics Communications
 SIAM Journal of Numerical Analysis
 SIAM Journal of Scientific Computing
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