titanium            package:DierckxSpline            R Documentation

_t_i_t_a_n_i_u_m _h_e_a_t _d_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

     49 values expressing a thermal property of titanium.

_U_s_a_g_e:

     data(titanium)

_F_o_r_m_a_t:

     a data.frame with the following columns:


   _x Temperature (in unknown units.  The primary source, de Boor and
        Rice (1968), does not say.  However, standard practice with
        these kinds of experimens would be to record data like this in
        degrees Kelvin, and the numbers seem consistent with that
        practice.)

   _y physical property

   _y_h_a_t predictions from some method

   _r_e_s_i_d_u_a_l 100*(y-yhat)

_D_e_t_a_i_l_s:

     Famous example used by de Boor and Rice (1968), Jupp (1978),
     Dierckx (1993) and perhaps others.  (de Boor and Rice do not
     mention the source nor provide other information on the units or
     how the data were collected.)

_S_o_u_r_c_e:

     de Boor, C., and Rice, J. R. (1986), Least-squares cubic spline
     approximation.  II:  variable knots.  _Report CSD TR 21_, Purdue
     U., Lafayette, IN.  (available from http://
     citeseer.ist.psu.edu/cache/papers/cs/24666/
     ftp:zSzzSzftp.cs.wisc.eduzSzApproxzSztr21.pdf/ deboor68least.pdf; 
     accessed 2008.07.22)

     Dierckx, Paul (1993), _Curve and Surface Fitting with Splines_,
     Springer.

     Jupp, D. L. B. (1975), _Approximation to data by splines with free
     knots_, SIAM Journal on Numerical Analysis, 15: 328-343.

_E_x_a_m_p_l_e_s:

     data(titanium)
     r <- curfit.free.knot(titanium$x2,
        titanium$y, g = 10, eps = 5e-4)
     xyplot(r, show.knots = TRUE)

