01006850

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01006850 Fedorov, Valery V. Hackl, Peter Optimal experimental design: Spatial sampling. Nova J. Math. Game Theory Algebra 4, No.1, 55-78 (1996). 1996 Nova Science Publishers, Commack, NY EN surface interpolation optimal sampling optimal location of supporting points covariance analysis most informative subsets regression survey evaluation estimation approximation of functions finite number of supporting points This survey is mainly devoted to the problems related to evaluation, estimation, and approximation of functions (or some functionals of them) which can be observed (measured) at a finite number of supporting points located on some (usually two dimensional) surface. Two cases can be distinguished. In the first one a function can be observed only once at every supporting point. Statistical geology provides the most typical examples for this case. In the second case observations (or measurements) can be done during some time interval. This type of experiment is mainly found in meteorology and environmetrics. Both cases are considered in the paper with the main emphasis on the problem of optimal location of the supporting points (i.e., the points where observations have to be made). In spite of the long history of the development of this problem the available results are rather sparse and are not systemized.