For the linear equation $$ Ax=b, $$ where $A$ is a 100 x 64 matrix, $b$ is a 100 x 1 vector, $x$ is a 64 x 1 vector, unknown. In my situation, x consists of no more than 5 Gaussian basis. $$ x=\Sigma_{i=1}^5 F_i \exp\left(-\frac{(T-T \mathrm{mean}_i)^2}{W_i}\right) $$ Here T is a known 64 x 1 vector, $W_i$ controls the width of the distribution and $F_i$ is the amplitude of the Gaussian basis. $F_i$, $W_i$ and $T\mathrm{mean}_i$ are undetermined parameters.
$A$,$b$,$T$ are attached here.
What I am interested in is the $T\mathrm{mean}_i$, i.e. the number of Gaussian basis and the center of the existing Gaussian ($A_i>0$).