Small Superposition Dimension and Active Set Construction for\n Multivariate Integration Under Modest Error Demand

2017/03/02 by Alexander D. Gilbert, Gilbert, Alexander D., Wasilkowski, Greg W.
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Manufacturing Process and Optimization #Mathematical Approximation and Integration #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1703.00985

openalex publication_date 2017/03/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Constructing active sets is a key part of the Multivariate Decomposition\nMethod. An algorithm for constructing optimal or quasi-optimal active sets is\nproposed in the paper. By numerical experiments, it is shown that the new\nmethod can provide sets that are significantly smaller than the sets\nconstructed by the already existing method. The experiments also show that the\nsuperposition dimension could surprisingly be very small, at most 3, when the\nerror demand is not smaller than 10^-3 and the weights decay sufficiently\nfast.\n

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