mwang@watmath.UUCP (mwang) (06/08/84)
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_S_E_M_I_N_A_R _A_C_T_I_V_I_T_I_E_S
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- Tuesday, June 12, 1984.
Dr. Kes Salkauskas of the University of Calgary will
speak on ``Weighted C sup 1 Splines for Automatic or
Interactive Interpolation.''
TIME: 2:30 PM
ROOM: MC 6091a
ABSTRACT
Especially in the interpolation of rapidly varying
univariate data by C sup 2 cubic splines, one often
obtains rather oscillatory interpolants. In order to
remedy this to some extent, we consider interpolation
with C sup 1 piecewise cubics s that minimize a
weighted semi-norm of the form ^ from a to b w(s prime
prime ) sup 2 . The weight function w can be chosen to
reduce oscillations. There is some simplification if
the weight function is piecewise constant on the parti-
tion of ( a, b) created by the knots. In that case a
discontinuity in the weight function at a knot controls
the discontinuity of the second derivative there. We
give examples of curves produced by an automated choice
of weight function, the effect of smoothing of w by
convolution, and some results when w is adjusted in an
interactive mode of operation.
June 8, 1984