table model updates [corrected]

[had "paramset" where I meant "table model"]

Sri asked that I send out an e-mail detailing the substantive
changes between the last table model proposal that was sent
to the list and the actual material added to the LRM draft f.

* the table model proposal from Martin had multi-dimensional
arrays, which are not part of AMS; he said I could remove
this feature from table model and wait for m-d arrays to
be added to AMS.

* splines have extra degrees of freedom; the following
paragraph was added to address this:

  For both quadratic and cubic interpolation, extra constraints
  are necessary to generate a unique spline over the supplied
  data points. For quadratic interpolation, Lagrange
  interpolation is used to fit a quadratic polynomial over the
  first three data points (those with lowest coordinate values);
  the second derivative of this polynomial is used to specify
  the second derivative of the quadratic spline at the first
  data point. For cubic interpolation, Lagrange interpolation
  is used to fit a cubic polynomial over the first four data
  points and the last four data points, and this polynomial
  is used to determine the second derivative of the cubic
  spline at the first and last data points. If there are not
  enough data points, the second derivatives are assumed to be
  zero.

Note that this differs from the "natural" cubic spline, but
gives the user the flexibility to control the derivative at
the endpoints by adding extra points.

-- 
Geoffrey J. Coram, Ph.D.    Senior CAD Engineer     
Analog Devices, Inc.        Geoffrey.Coram@analog.com 
804 Woburn St., MS-422,     Tel (781) 937-1924
Wilmington, MA 01887        Fax (781) 937-1014