Comprehensive Tikhonov Regularization Algorithm Implementation

This article presents a comprehensive discussion of the Tikhonov regularization algorithm, including both standard implementations and iterative variants. Notably, the paper provides detailed numerical examples with code implementation insights to help readers better understand practical applications of these algorithms. We emphasize that these examples are designed to demonstrate algorithm application scenarios and enhance learning effectiveness through hands-on implementation approaches. For standard Tikhonov regularization, we typically implement the minimization of ||Ax - b||² + λ||x||² using matrix inversion or singular value decomposition (SVD) techniques. The iterative version often employs conjugate gradient methods or Landweber iteration with adaptive regularization parameter selection. If you're interested in this topic, we recommend carefully studying this paper and examining the numerical examples in depth to gain thorough understanding of Tikhonov regularization algorithm implementations, including practical considerations for parameter tuning and convergence analysis.