TY - JOUR
T1 - Best Near-Interpolation by Curves: Existence
AU - Kersey, Scott
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PY - 2000
Y1 - 2000
N2 - The conditions derived in [K. Scherer and P. W. Smith, SIAM J. Numer. Anal. , 20 (1989), pp. 160--168] for the existence of minimizers to the nonlinear problem of best "interpolation" by curves are extended to the problem of best "near-interpolation" by curves that meet arbitrary sets, such as closed balls (as in [S. Kersey, Best Near-Interpolation by Curves: Optimality Conditions , Technical Report 99-05, Center for the Mathematical Sciences, University of Wisconsin, Madison, WI, 1999]). The minimizers are spline curves with breakpoints at the data sites at which the curves meet the sets, and the nonlinearities arise as these data sites vary from curve to curve. The results here apply to Hermite-type interpolation conditions, with the possibility of repeated data sites.
AB - The conditions derived in [K. Scherer and P. W. Smith, SIAM J. Numer. Anal. , 20 (1989), pp. 160--168] for the existence of minimizers to the nonlinear problem of best "interpolation" by curves are extended to the problem of best "near-interpolation" by curves that meet arbitrary sets, such as closed balls (as in [S. Kersey, Best Near-Interpolation by Curves: Optimality Conditions , Technical Report 99-05, Center for the Mathematical Sciences, University of Wisconsin, Madison, WI, 1999]). The minimizers are spline curves with breakpoints at the data sites at which the curves meet the sets, and the nonlinearities arise as these data sites vary from curve to curve. The results here apply to Hermite-type interpolation conditions, with the possibility of repeated data sites.
KW - approximation
KW - interpolation
KW - near-interpolation
KW - parametric curves
KW - splines
UR - https://doi.org/10.1137/S0036142999355696
U2 - 10.1137/S0036142999355696
DO - 10.1137/S0036142999355696
M3 - Article
SN - 0036-1429
VL - 38
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
ER -