In this paper, we consider the problem of finding approximate inverses of a given matrix. We give an explicit solution to the rank-constrained regularized inverse approximation problem and obtain an inverse-regularized Eckart-Young-like theorem.
Chung, J., Chung, M., & O’Leary, D. P. (2015). Optimal regularized low rank inverse approximation. Linear Algebra and Its Applications, 468, 260–269. https://doi.org/10.1016/j.laa.2014.07.024