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In 1992, in a famous paper, Deville and Särndal proposed the calibration method in order to adjust samples on known population totals. This paper had a very important impact in the theory and practice of survey statistics. In this paper, we propose a rigorous formalization of the calibration problem viewed as an optimization problem. We examine the main calibration functions and we discuss the question...
This rejoinder refers to the comments available at: https://doi.org/10.1007/s11749-019-00682-2 ; https://doi.org/10.1007/s11749-019-00683-1 ; https://doi.org/10.1007/s11749-019-00684-0 ; https://doi.org/10.1007/s11749-019-00686-y ; https://doi.org/10.1007/s11749-019-00687-x .
A new space–time finite element method for the solution of parabolic partial differential equations is introduced. In a mesh and degree-dependent norm, it is first shown that the discrete bilinear form for the space–time problem is both coercive and continuous, yielding existence and uniqueness of the associated discrete solution. In a second step, error estimates in this mesh-dependent norm are derived...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB–ANOVA–RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming...
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