Regularized Least-Squares ProblemLeast-Squares > Definitions >> [ LS | Regularized LS | Constrained LS ] | Solution | Sensitivity | Limitations
Regularized least-squaresIn the case when the matrix The regularized least-squares problem has the form ![]() where Expression as an ordinary LS problemThe regularized problem can be expressed as an ordinary least-squares problem, where the data matrix is full column rank. Indeed, the above problem can be written as the ordinary LS problem ![]() where ![]() The presence of the identity matrix in the SolutionSince the data matrix in the regularized LS problem has full column rank, the formula seen here applies. The solution is unique, and given by ![]() For The above formula explains one of the motivations for using regularized least-squares in the case of a rank-deficient matrix |