Some New Convergence Analysis and Applications of POD-Greedy Algorithms

2024/07/13 by Yuwen Li, Yupeng Wang, Li, Yuwen +1 · 1 citation
Computer Science · #FOS: Mathematics #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2407.09933

openalex publication_date 2024/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we derive a novel convergence estimate for the weak POD-Greedy method with multiple POD modes and variable greedy thresholds in terms of the entropy numbers of the parametric solution manifold. Combining the POD with the Empirical Interpolation Method (EIM), we also propose an EIM-POD-Greedy method with entropy-based convergence analysis for simultaneously approximating parametrized target functions by separable approximants. Several numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm compared to traditional methods.

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