BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-77-636
       ENTRY:: June 28, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: $C^m$ convergence of trigonometric interpolants
        TYPE:: Technical Report
      AUTHOR:: Bube, Kenneth P.
        DATE:: October 1977
       PAGES:: 28
    ABSTRACT:: For m $\geq$ 0, we obtain sharp estimates of the uniform
               accuracy of the m-th derivative of the n-point trigonometric
               interpolant of a function for two classes of periodic
               functions on R. As a corrollary, the n-point interpolant of a
               function in $C^k$ uniformly approximates the function to
               order o($n^{1/2-k}$), improving the recent estimate of
               O($n^{1-k}$). These results remain valid if we replace the
               trigonometric interpolant by its K-th partial sum, replacing
               n by K in the estimates.
       NOTES:: [Adminitrivia V1/Prg/19950628]
         END:: STAN//CS-TR-77-636