Are such contests silly?  Yes, unless you are modelling the universe.
Then you need better hardware.

Does J reduce thinking time?  Not really in this case.  J and MATLAB
have builtin functions for matrix multiplication and inversion.  If
you were writing in C, you would need a bit more thinking time for
matrix multiplication and a lot more for inversion.

Even though it is heresy, it may be the case that MATLAB can do
matrix multiplication faster than J.  The reason is the BLAS (Basic
Linear Algebra Subprograms), used for linear algebra in scientific
computing (for example, it underpins LAPACK).  The BLAS is tuned to
a particular CPU chip, since the algorithm used may depend on cache
size, ability to pipeline, etc.  Some versions will fine tune
themselves from the actual system.

MATLAB makes a big point of this, for example a feature of version 7.5
is

Upgraded Linear Algebra Package library (LAPACK 3.1) on all platforms,
plus upgraded optimized Basic Linear Algebra Subprogram libraries
(BLAS) on AMD processors (AMCL 3.6)

Best wishes,

John


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