报告人：孟宇煌 博士（代尔夫特理工大学）

时间：2026年02月02日 15:30-

地址：数统学院LD718

摘要：Linear and nonlinear equation systems emerge in a wide range of real-world applications. For large linear systems, iterative solvers are generally preferred over direct methods due to the latter's superlinear growth of computational and memory costs. Although convergence theories and preconditioners are well-developed under certain matrix assumptions, many system classes still pose open challenges. For nonlinear systems, the Newton's method, for example, may converge quadratically near the solution but can also converge slowly or diverge for inappropriate initial guesses. A wide variety of solvers exists, with various variants and hyperparameters, and developing efficient and robust iterative methods remains an active research area. Recently, machine learning (ML) techniques have emerged as a promising approach to enhance the efficiency of classical iterative methods while preserving their interpretability and reliability. We refer to these ML-enhanced iterative methods as hybrid iterative methods, in the sense that they integrate classical iterative frameworks with ML-based components. This paper provides a comprehensive overview of the state-of-the-art approaches for constructing hybrid iterative methods for both linear and nonlinear equation systems.

邀请人：数学研究中心

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