[submit] gsl_interp_polynomial, gsl_polynomial types

[Brian Gough]

Dan, Ho-Jin writes:
 > I have a trouble in building cvs sources as
 >  Making all in interpolation make[2]: Entering directory
 > `/usr/local/gnu/src/cvs/gsl/interpolation' make[2]: *** No rule to
 > make target `poly.c', needed by `poly.lo'.  Stop.  make[2]: Leaving
 > directory `/usr/local/gnu/src/cvs/gsl/interpolation' make[1]: ***
 > [all-recursive] Error 1 make[1]: Leaving directory
 > `/usr/local/gnu/src/cvs/gsl' make: *** [all-recursive-am] Error 2
 >  poly.c couldn't be found in the cvs tree. what's wrong?

I forgot to do 'cvs add'.  It should be available now.

 > By the way, I found the line search (one dimensional min.) routines
 > are difficult to use in the multidimensional optimization. For
 > example, gsl supplied unconstraint min. routines have its own
 > directional minimizer.  I have also similar one for me (quadratic
 > or brent minimizer).  One-D directional minimizers seems to be
 > collected into one-dimensional minimization category which has
 > routines for minimizing f(x) on [a, b] and finding the interval [a,
 > b]. I think that one-D directional minimizer is carefully organized
 > to minimizer the number of the object function call, practically,
 > calling objective function are expensive except the mathematical
 > functions.

Right, too much communication is required to use the 1-d minimization
routines. It's better to make the line minimization part of the
overall multidimensional algorithm.

 > I attache the experimental source for directional search.  in
 > min_quad.c, commented out main funcition has simple usage for it.
 > for complex application, steepest-descent.c is provided.  in
 > summary, directional line search controlled with the trial step
 > size is needed in the future.