Tikhonov Regularization Method

Tikhonov.m implements the Tikhonov regularization method, a technique for solving linear inverse problems. This approach adds a regularization term to constrain the solution, preventing overfitting or underfitting issues and resulting in more robust models. The mathematical formulation of Tikhonov regularization is expressed as:


In this formulation, λ represents the regularization parameter, A is the coefficient matrix of the linear problem, x is the solution vector, and b is the right-hand side vector. By adjusting the value of λ, one can control the regularization strength to obtain different solutions. The implementation typically involves solving the augmented normal equations (AᵀA + λI)x = Aᵀb using matrix decomposition techniques like SVD or Cholesky factorization for numerical stability.

Tikhonov regularization serves as a powerful tool widely applied in signal processing, statistics, and machine learning domains, particularly useful for ill-posed problems where small perturbations in input data may cause large solution variations.