13. Compositional Differential Calculus on the Simplex

  1. Vera Pawlowsky-Glahn1 and
  2. Antonella Buccianti2
  1. Carles Barceló-Vidal,
  2. Josep Antoni Martín-Fernández and
  3. Glòria Mateu-Figueras

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch13

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Barceló-Vidal, C., Martín-Fernández, J. A. and Mateu-Figueras, G. (2011) Compositional Differential Calculus on the Simplex, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch13

Editor Information

  1. 1

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 2

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. Department of Computer Science and Applied Mathematics, University of Girona, Spain

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462

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Keywords:

  • compositional differential calculus on simplex - basic mathematical concepts;
  • new concept of compositional derivative - of a function, on the simplex, with simplicial operators;
  • vector-valued functions on the simplex – CODA, scale-invariant principle;
  • C-derivatives on the simplex - topics of compositional differential calculus;
  • directional C-derivatives;
  • critical points of C-differentiable real-valued function on Sn - topology induced in Sn by Euclidean metric structure;
  • polynomial of degree one;
  • polynomial of degree one in logarithms;
  • response of interest, thread elongation η of yarn - measured in kilograms of force applied

Summary

This chapter contains sections titled:

  • Introduction

  • Vector-Valued Functions on the Simplex

  • C-Derivatives on the Simplex

  • Example: Experiments with Mixtures

  • Discussion

  • Acknowledgements

  • References