Shape preserving approximation using least squares splines

  • Gleb Beliakov


Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.


Aggregation Operator Spline Approximation Polynomial Spline Underlying Function Linear Spline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer 2000

Authors and Affiliations

  • Gleb Beliakov
    • 1
  1. 1.School of Computing and MathematicsDeakin UniversityClaytonAustralia

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