近似理论家视角下的求解算子方程
An Approximation Theorist's View on Solving Operator Equations
AI总结：
本文从近似理论角度探讨求解偏微分方程和算子方程的问题，分析有限元、雷利-里茨等方法的本质，并展示如何利用近似理论解决稳定性问题。
摘要：
当近似理论家审视well-posed PDE问题或算子方程，以及有限元、雷利-里茨或特雷弗茨技术、基本解或特解方法及其组合时，这些标准求解算法本质上都转化为近似问题和稳定性问题。这些问题可以通过近似理论来处理，本文展示了如何做到这一点，并特别应用于上述算法。目的是让远离该领域的读者能通过近似理论家的视角获得帮助。
英文摘要：
When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh-Ritz or Trefftz techniques, methods of fundamental or particular solutions and their combinations, they boil down to approximation problems and stability issues. These two can be handled by Approximation Theory, and this paper shows how, with special applications to the aforementioned algorithms. The intention is that the Approximation Theorists viewpoint is helpful for readers who are somewhat away from that subject.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
