演講公告

新聞標題：　( 2026-04-16 )

• 演講主題：Newton-Type Methods, Stiffness, and Nonlinear Preconditioning: A Dynamical View

• 主講人：黃楓台 處長 (國家太空中心)

• 演講日期：2026年4月28日(二) 14:20 –15:20

• 演講地點：(光復校區) 科學一館213室

• 摘要內容：
  

  Abstract. Newton-type methods are among the most effective tools for solving large-scale nonlinear systems arising in scientific computing. Despite their fast local convergence, their global behavior can be unpredictable, with common issues such as overshooting, stagnation, and sensitivity to problem scaling—especially in stiff or highly unbalanced systems.
  
  In this talk, we present a dynamical systems perspective for understanding these behaviors by interpreting Newton iterations as discrete approximations of an underlying continuous-time flow. This viewpoint provides an intuitive characterization of nonlinear imbalance in terms of stiffness, offering insight into why classical globalization strategies, particularly line search, may become ineffective or overly restrictive.
  
  Motivated by this perspective, we revisit line search methods and introduce improved strategies, including curve search techniques, that better align with the intrinsic dynamics of the nonlinear system. We further show that nonlinear preconditioning can be naturally interpreted as a transformation that reduces stiffness and restores balance, leading to improved robustness and convergence.
  
  Numerical examples from nonlinear PDEs illustrate how this framework not only enhances performance, but also provides a unified viewpoint for understanding globalization, acceleration, and stabilization in Newton-type methods.

• 相關檔案：Talk_1150428-2.pdf

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