论文标题
关于矩阵方程的溶解度$（1+ae^{ - \ frac {\ | x \ |} {b}}）x = y $
On the solvability of the matrix equation $(1+ae^{-\frac{\|X\|}{b}})X=Y$
论文作者
论文摘要
处理后的矩阵方程$（1+ae^{ - \ frac {\ | x \ |} {b}}} {b}}）x = y $中的x = y $起源于建模方法，以描述橡胶的非线性时间相关机械行为。我们对$（1+ae^{ - \ frac {\ | x \ |} {b}}}）x = y $的$（1+ae^{ - \ frac { - \ frac { - \ frac { - \ frac { - \ |参数$ a，b \ in \ mathbb {r} $，$ b \ neq 0 $，并给出算法以数值计算其解决方案，以$ e = \ m athbb {r}^{m \ times n} $，$ m，$ m，$ m，n \ in \ in \ in \ in \ mathbb {n} n} $，$ n} $，n} $ n ob fr fr frofe frofe fr frof。
The treated matrix equation $(1+ae^{-\frac{\|X\|}{b}})X=Y$ in this short note has its origin in a modelling approach to describe the nonlinear time-dependent mechanical behaviour of rubber. We classify the solvability of $(1+ae^{-\frac{\|X\|}{b}})X=Y$ in general normed spaces $(E,\|\cdot\|)$ w.r.t. the parameters $a,b\in\mathbb{R}$, $b\neq 0$, and give an algorithm to numerically compute its solutions in $E=\mathbb{R}^{m\times n}$, $m,n\in\mathbb{N}$, $m,n\geq 2$, equipped with the Frobenius norm.
