Constructionof robust estimates of meano values and variations of two-dimensional data on thebasis of the spectral matrix norm

The problem of estimating of mean values and variations of two-dimensional data is considered.Data can be represented as a matrix in discrete case, or as a function of two variables in thecontinuous case. Estimate of the mean value of discrete data is found as solution of the optimizationproblem with objective function in the form of the spectral norm of a matrix. In the continuouscase the problem is reduced to the discrete case by sampling the domain of function. The inequalitiesto assess the influencet of errors in the data matrix on the results of calculations of meanvalues and variations in data are derived. The results of test calculations confirm the robustness ofthe estimates of the mean values and variations derived from spectral norms with respect to dataerrors.

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