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Shape preserving histogram approximation

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Abstract

We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of quadratic-like splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the Boolean sum of univariate B-splines and show that for a proper choice of the degrees, the splines are positive and satisfy local monotonicity constraints.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, Università degli Studi di Siena, Pian dei Mantellini, 44, 53100, Siena, Italy

    Paolo Costantini & Francesca Pelosi

Authors
  1. Paolo Costantini
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  2. Francesca Pelosi
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Corresponding author

Correspondence to Paolo Costantini.

Additional information

Communicated by J. Carnicer and J.M. Peña

Dedicated to Prof. Mariano Gasca in occasion of his 60th birthday

Supported by Università di Siena, under P.A.R. 2002.

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Costantini, P., Pelosi, F. Shape preserving histogram approximation. Adv Comput Math 26, 205–230 (2007). https://doi.org/10.1007/s10444-004-8008-2

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  • DOI: https://doi.org/10.1007/s10444-004-8008-2

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