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Numerical algorithms for problems in analysis and algebra, scientific computation
2
votes
0
answers
47
views
Numerically Evaluate the limit of the solution of a functional equation
I need to evaluate the limit of $f(x)$ as $x\to0$, where the function $f$
solves the following equation:
$$
f(x)=\left\{
\begin{array}{ll}
g(x) & \text{if } x\geq \frac{1}{2};\\
\frac{1}{2} f(\alpha …
4
votes
1
answer
188
views
Complexity of finding one vertex of a nonempty polytope
Let $P$ be a polytope given by some half-space description: $P=\{x\in\mathbb{R}^n: Ax\leq b\}$ for some $A\in\mathbb{R}^{m\times n}, b\in\mathbb{R}^m$, $m\geq n$. Assume that $x_0\in P$ for some given …