Numerical Approximation of Real Functions and One Minkowski's Conjecture on Diophintine Approximations
Nikolaj M. Glazunov
在本周文中,我考虑了几种实际函数的近似值,以验证计算(可可靠计算)的问题,即隐含定义的真实函数 x_n+1 = G(x_1,..., x_n),其中依赖性F(x_1,...,x_n+1) = 0在某些紧凑域上通过足够平滑的真实函数F(x_1,...,x_n+1)>定义。 构造版本的Kolmogorov-Arnold和隐式函数定理,关于浮点近似的结果,浮点近似的结果,这些近似值给出了一些真实函数的下界和上行估计,以及近似代数计算用于目的。 严谨的理论可以建立在浮点域的歧位数分析的基础上。 在文中,我们展示了我们对闵可夫斯基对该地区关键决定因素的猜想的示例的方法 | x |^p + |^p ≤ 1, p > 1.
In this paper I consider the applications of several kinds of approximations of real functions to the problem of verified computation (reliable computing) of the range of implicitly defined real function x_n+1 = G(x_1, ..., x_n), where dependency F(x_1, ..., x_n+1) = 0 is defined on some compact domain by a sufficiently smooth real function F(x_1, ..., x_n+1) >. Constructive version of Kolmogorov-Arnold and implicit function theorems, results about floating-point approximation, floating-point ap...
