Sensitivity of low-rank matrix recovery

Algebraic compressed sensing

“…If the data point is y ̸ ∈ µ(X ) and if one seeks to solve the least squares minimization problem min x∈X 1 2 ∥µ(x) − y∥ 2 , then the condition number of this alternative problem is determined both by the condition number of µ −1 and the curvature of µ(X ) at µ(x); see [92] for more precise statements. For the case where X is the variety of low-rank matrices, the condition number of the associated least-squares problem was worked out in detail in [93].…”

“…The Julia code we used is attached as an ancillary file and available at[103]. The experiments were performed in Julia v1.6.2 on a computer running Ubuntu 20.04.2 LTS consisting of an Intel Core i7-4770K CPU (4 cores, 3.5GHz clockspeed) with 32GB of main memory.…”