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$$X=\begin{bmatrix} | & | & & | \\ x_1 & x_2 & \dots & x_m \\ | & | & & | \end{bmatrix} =U\Sigma V^T =\begin{bmatrix} | & | & & | \\ u_1 & u_2 & \dots & u_n \\ | & | & & | \end{bmatrix} \begin{bmatrix} \sigma_1 & & \\ & \ddots & \\ & & \sigma_m \\ & & \end{bmatrix} \begin{bmatrix} \text{---} & v_1^T & \text{---} \\ \text{---} & v_2^T & \text{---} \\ \text{---} & \vdots & \text{---} \\ \text{---} & v_m^T & \text{---} \end{bmatrix}$$

where $n$ is the number of points in each $x$, and $m$ is the number of $x$ values.

This can be further expanded into

$$ X = \sigma_1 u_1 v_1^T + \sigma_2 u_2 v_2^T + \ldots + \sigma_m u_m v_m^T$$ (assuming $n>>m$).

We can therefore select the first $r$ terms of this expansion to get a reduced-order approximation of X. I.e. $$ X \approx \tilde{U}\tilde{\Sigma}\tilde{V}^T$$.