All Questions

I have a question about linear approximation in the multivariate case.\ Let $f:B^d_r\to \mathbb{R}$ be a real-valued $C^2$-function defined on the $d$-dimensional ball of radius $r$ centered at the ...

Let $\delta, \varepsilon \in (0,1)$. I am interested in a sequence $\{f_n\}$ of polynomial approximations of the square root function $x \to x^{1/2}$ on $[\delta,1]$, of the form $$ f_n(x) = \sum_{i=0}...

Let $k,n,m$ be positive integers and suppose that $f$ is $C^{k}(\mathbb{R}^n,\mathbb{R}^m)$ functions. For any given $\epsilon>0$ and $x_0\in \mathbb{R}^n$, are there known sharp approximation ...

I am trying to prove equations (3) given in this paper http://users.cecs.anu.edu.au/~thush/publications/vtc_final.pdf. The authors use taylor series to approximate function $f(q) = \left(1 + q \...

Suppose $Y$ and $Z$ two random variables, $\lambda \in \mathbb{R} $. We note $F^{-1}_{Y}(\alpha)$ the quantile function of the variable $Y$ at the quantile level $\alpha \in (0,1)$. Do you have any ...

Firstly, I have to say that I don't understand Padé approximation well. But I discovered that, it is more precise than Taylor series. I have to create approximation for these functions: Log(x) and ...