How to Smooth Curves and Surfaces with Splines and Cross-Validation

Abstract

The use of smoothing splines and the method of generlized cross validation (GCV) for smoothing discrete noisy data from an unknown but smooth curve is reviewed. The use of 'plaque mince' or Laplacian smoothing splines with GCV for smoothing discrete noisy data from an unknown but smooth surface is described. A numerical algorithm for this (non-trivial) computational problem is described, and an example from a Monte Carlo study is presented to show how the method works on simulated data. The results are extremely promising. Some design problems are briefly mentioned. Some conjectures are made concerning optimality properties of Laplacian smoothing splines and Laplacian histosplines.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1979
Accession Number
ADA068430

Entities

People

  • Grace Wahba

Organizations

  • University of Wisconsin Madison Department of Statistics

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Data Science
  • Information Science
  • Instructions
  • Mathematics
  • Security
  • Statistics
  • Triangles
  • Universities
  • Validation

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Modeling and Simulation