Digital Nets and Sequences for Quasi-Monte Carlo Methods

2022/07/27 by Hee Sun Hong, Hong, Hee Sun
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Software (cs.MS) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2207.13802

openalex publication_date 2022/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results pertaining to digital nets and sequences: implementing randomized digital nets, finding the distribution of the discrepancy of scrambled digital nets, and obtaining better quality of digital nets through evolutionary computation. Finally, applications of scrambled and non-scrambled digital nets are provided.

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