力学与实践 ›› 2020, Vol. 42 ›› Issue (6): 832-836.DOI: 10.6052/1000-0879-20-191

• 小问题 • 上一篇    下一篇

从希尔伯特的第13问题谈起1)

林永静2)   

  1. 温州职业技术学院建筑工程系,浙江温州 325035
  • 收稿日期:2020-05-08 修回日期:2020-09-04 出版日期:2020-12-20 发布日期:2020-12-23
  • 通讯作者: 2)林永静,讲师,研究方向为计算力学。E-mail: linyongjing@mail.tsinghua.org.cn
  • 基金资助:
    1) 浙江省教育厅科研项目(Y201636870) 和浙江省自然科学基金项目(LY20E080017) 资助。

TALK STARTED FROM HILBERT'S 13TH PROBLEM1)

LIN Yongjing2)   

  1. Department of Architectural Engineering, Wenzhou Vocational Technical College, Wenzhou 325035, Zhejiang, China
  • Received:2020-05-08 Revised:2020-09-04 Online:2020-12-20 Published:2020-12-23

摘要: 希尔伯特第13问题启发了一个多元函数可以用有限个一元函数来表示的思路。研究发现,众多工程问题如高维数烦恼的研究均导源于希尔伯特第13问题。本文沿着希尔伯特第13问题启发的思路,对解决高维数烦恼进行了探索,提出了延拓Kantorovich法的解决方案。数值结果表明,延拓Kantorovich法是用一元函数逼近多元函数的一种有效途径,不失为高维数烦恼的一种有发展潜力的解决方案。

关键词: 希尔伯特第13问题, 多元函数, 高维数烦恼, 延拓Kantorovich法

Abstract: Hilbert's 13th Problem says that a multivariate function can be represented by a few univariate functions. It has been found that a number of engineering problems, such as the high dimension trouble, are derived from Hilbert's 13th Problem. With the enlightenment of Hilbert's 13th Problem, this paper explores how to solve the problem of the high dimension trouble and puts forward the means of extending the Kantorovich method. Numerical results show that the extended Kantorovich method is an effective approach for approximating a multivariate function using univariate functions and it is a solution having a potentiality for solving the high dimension trouble.

Key words: Hilbert's 13th Problem, multivariate function, high dimension trouble, extended Kantorovich method

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