论文标题
计算截短的关节近似本本基基，以减少模型订单
Computing Truncated Joint Approximate Eigenbases for Model Order Reduction
论文作者
论文摘要
在本文档中，介绍了该理论和算法的某些要素，这些要素与矩阵有限集合的近似关节本特征的存在和计算性相对应，并提出了用于降低模型订单的应用。更具体地说，给定有有限的集合$ x_1，\ ldots，x_d $ hermitian矩阵中的$ \ mathbb {c}^{n \ times n} $，一个积极的整数$ r \ ll n $，以及副本数量$ \ hat {x} $ {x} _ { j \ leq d $，$ 1 \ leq k \ leq r $。首先，我们研究一组$ r $ vectors $ w_1的可计算性\ Mathbb {C}^n} \ sum_ {j = 1}^d \ | x_jw- \ hat {x} _ {x} _ {j，j，k} w \ |^2 $对于每个$ 1 \ leq k \ leq r $一些原型算法以及一些数字示例也会提出。
In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection $X_1,\ldots,X_d$ of Hermitian matrices in $\mathbb{C}^{n\times n}$, a positive integer $r\ll n$, and a collection of complex numbers $\hat{x}_{j,k}\in \mathbb{C}$ for $1\leq j\leq d$, $1\leq k\leq r$. First, we study the computability of a set of $r$ vectors $w_1,\ldots,w_r\in \mathbb{C}^{n}$, such that $w_k=\arg\min_{w\in \mathbb{C}^n}\sum_{j=1}^d\|X_jw-\hat{x}_{j,k} w\|^2$ for each $1\leq k \leq r$, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well.
