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Accurate emulators for large-scale computer experiments. (English) Zbl 1246.65172

Summary: Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and numeric portions. Bounds on the numeric and nominal error are developed to show theoretically that substantial gains in overall accuracy can be attained with the multi-step approach.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
65G50 Roundoff error

Software:

Matlab; mlegp
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