A parallel approximation algorithm for positive linear programming

We show that if a polynomial $f\in \mathbb{R}[x_1,\ldots,x_n]$ is nonnegative on a closed basic semialgebraic set $X=\{x\in\mathbb{R}^n:g_1(x)\ge 0,\ldots,g_r (x)\ge 0\}$, where $g_1,\ldots,g_r\in\mathbb{R}[x_1,\ldots,x_n]$, then $f$ can be approximated ...

Linear programming and least squares computations are accelerated using author's parallel algorithms for solving linear systems. The implications on the performance of the Karmarkar and the simplex algorithms for dense and sparse linear programs are ...

Let $(\Omega ,\mathcal{F},\mathbb{P})$ be a probability space with a Brownian motion $\{ \beta (t):t \geqq 0\} $. Let S be the space of functions $a(t) \in C^1 [0,\infty )$ such that $e^{ - \lambda t} a(t) \in L^1 (0,\infty )$ for all $\lambda > 0$. A ...