Least-squares via SVD: beta-hat = V Sigma^+ U^T y; Frobenius-norm extremum

Least-squares via singular-value decomposition (SVD) framework (Eckart-Young 1936; Golub-Reinsch 1970). Setup: linear regression problem X beta = y with X in R^{m x n} (m >= n), y in R^m, finds beta minimising ||X beta - y||_2. SVD of X =…