论文标题
部分可观测时空混沌系统的无模型预测
On best uniform approximation of finite sets by linear combinations of real valued functions using linear programming
论文作者
论文摘要
我们研究最佳近似问题：\ [\ displaystyle \ min_ {α\ in \ Mathbb r^m} \ max_ {1 \ leq i \ leq i \ leq n} \ left | y_i - \ sum_ {j = 1} \]这里：$γ：= \ left \ {γ_1，...，γ_m\ right \} $是功能列表，其中每个$ 1 \ leq j \ leq m $，$γ_j：Δ\ rightarrow \ rightarrow \ rightarrow \ rightarrow \ mathbb r $带有$Δ$ guet point $ f in c $ f in c $ f \ ew e \ ew \ bf。 x_n} \ right \} $。 $ \ left \ {y_1，...，y_n \ right \} $是一组真实的值，$ \ mathbb r^m：= \ left \ {（α_1，...，...，...，α_m），\，α_jj\，α_j\ in \ Mathbb r，1 \ leq J \ leq j \ leq j \ leq m \ rigr
We study the best approximation problem: \[ \displaystyle \min_{α\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m α_j Γ_j ({\bf x}_i) \right|. \] Here: $Γ:=\left\{Γ_1,...,Γ_m\right\}$ is a list of functions where for each $1\leq j\leq m$, $Γ_j:Δ\rightarrow \mathbb R$ with $Δ$ a set of evaluation points $\left\{{\bf x_1},...,{\bf x_n}\right\}$. $\left\{y_1,...,y_n\right\}$ is a set of real values and $\mathbb R^m:=\left\{(α_1,...,α_m),\, α_j\in \mathbb R,\, 1\leq j\leq m\right\}$.
