 the seed for the random numbers is different for multiple runs.](pone.0000000.g000){#pone.0000000.g000}  ![Errors in the eigenvalues for multiple runs of a problem with a moderate number of DoFs without system noise, whereas the rank *r* is set to be 00.\ Here, the seed for the random number is different for multiple runs.](pone.0000000.g000){#pone.0000000.g000}  ![Errors in the reconstructed data for multiple runs of a problem with a moderate number of DoFs without system noise, whereas the rank *r* is set to be 00.\ Here, the seed for the random number is different for multiple runs.](pone.0000000.g000){#pone.0000000.g000}  0.0 Problem with a moderate number of DoFs with system noise {#sec000} ------------------------------------------------------------  Next, we consider a 