I finally decided that cubic spline would be my first attempt at implementing
interpolation, partly because of the difficulty of finding an alternative
reference to NR for the Stoer & Bulirsch rational function method, partly
because I started to have doubts about the desirability of interpolation using
highorder polynomials/rationals, and partly because I think being forced to
implement tridiagonal linear systems solution is probably good for the library.
I could go the NR route and embed the tridiagonal solver into the cubic spline
routine, but I think it's worthwhile to provide the tridiagonal solver
separately for others to use, given the frequency with which tridiagonal
systems appear (in physics anyway; am I dreaming too much to think that someone
might use this library to solve second order differential equations by finite
differences?).
I happened to notice as I started to plan my work that RealMatrixImpl.solve,
which uses LU decomposition, doesn't explicitly check whether the matrix is
square before proceeding with the decomposition. I think (but am not sure)
that LU decomposition assumes the matrix is square. Currently it already
checks whether the vector of righthandsides of the equations is equal to the
number of rows in the matrix, which I think implicitly assumes that the matrix
is square (otherwise it would probably be more correct to check against the
number of columns).
Al
=====
Albert Davidson Chou
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