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