Anchor Points Matter in ANOVA Decomposition
نویسندگان
چکیده
We focus on the analysis of variance (ANOVA) method for high dimensional approximations employing the Dirac measure. This anchored-ANOVA representation converges exponentially fast for certain classes of functions but the error depends strongly on the anchor points. We employ the concept of “weights per dimension” to construct a theory that leads to the optimal anchor points. We then present examples of a function approximation as well as numerical solutions of the stochastic advection equation up to 500 dimensions using a combination of anchored-ANOVA and polynomial chaos expansions.
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