## Abstract

When using least squares to fit the linear model of coregionalization to multivariate geostatistical data, the sill matrices for the different regions must be estimated, subject to the constraint that they be non-negative definite. In 1992, Goulard and Voltz proposed and empirically examined an iterative algorithm for doing this. Although no proof was given for its convergence or for the uniqueness of the solution to the problem, the algorithm has subsequently been extensively and successfully used. In this paper, we prove that the minimization problem, in fact, has a unique solution and that the algorithm is guaranteed to converge to it from any starting point. We also discuss the effect of the starting point on the speed of convergence.

Original language | English |
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Pages (from-to) | 15-27 |

Number of pages | 13 |

Journal | Mathematical Geosciences |

Volume | 41 |

Issue number | 1 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

## Keywords

- Algorithm
- Convergence
- Direct and cross semivariograms
- Linear model of coregionalization
- Quadratic functions

## ASJC Scopus subject areas

- Mathematics (miscellaneous)
- General Earth and Planetary Sciences