Knot selection for least squares approximation using thin plate splines.

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Author
McMahon, John R.
Date
1986-06Advisor
Franke, Richard
Second Reader
Schelin, Charles W.
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Show full item recordAbstract
Given a large set of scattered data (x(i),y(i) ,f(i)), a method for
selecting a significantly smaller set of knot points which will
represent the larger set is described, leading to a package of FORTRAN
subroutines. The selection of the knot point locations is based on the
minimization of the sum of the squares of the difference between the
average number of points per Dirichlet tile and the actual number of
points in each tile, subject to the constraint that each knot is
located at the centroid of its tile. The pertinent theoretical and
computational aspects of the subroutines are introduced and described in
detail. Using the least squares thin plate spline approximation method
for constructing surfaces, various test surfaces are examined and
compared to surfaces obtained using smoothing splines and the bicubic
Hermite approximation method. The FORTRAN subroutines are made
available to prospective users through a point of contact.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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