Module IV: Inverse Problems in Empirical Modeling

This module provides a comprehensive introduction to solving a variety of inverse problems: linear/nonlinear, over/under determined, deterministic/statistical, weighted/unweighted, batch/sequential modes. Two main approaches are covered: matrix-based decomposition using direct multiplicative methods (LU, LDLT, Cholesky, QR, SVD algorithms), and standard optimization methods (Gradient, Conjugate gradient, Quasi-Newton algorithms).