Fast and compact smoothing on large multidimensional grids

P. H C Eilers, Iain D. Currie, Maria Durbán

Research output: Contribution to journalArticlepeer-review

156 Citations (Scopus)


A framework of penalized generalized linear models and tensor products of B-splines with roughness penalties allows effective smoothing of data in multidimensional arrays. A straightforward application of the penalized Fisher scoring algorithm quickly runs into storage and computational difficulties. A novel algorithm takes advantage of the special structure of both the data as an array and the model matrix as a tensor product; the algorithm is fast, uses only a moderate amount of memory and works for any number of dimensions. Examples are given of how the method is used to smooth life tables and image data. © 2005 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)61-76
Number of pages16
JournalComputational Statistics and Data Analysis
Issue number1 SPEC. ISS.
Publication statusPublished - 10 Jan 2006


  • B-splines
  • Difference penalty
  • Multidimensional array
  • P-splines
  • Smoothing
  • Tensor product


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