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July 31, 2025

Least Squares Data Fitting with Applications

26 minutes

Focuses on least squares data fitting with a strong emphasis on numerical methods and statistical analysis. It explores various algorithms for solving linear and nonlinear least squares problems, including direct and iterative methods for both full-rank and rank-deficient scenarios. The discussion extends to constrained least squares, missing data imputation, and regularization techniques for ill-conditioned problems. Furthermore, the text examines diverse applications such as spline approximation, neural network training, and inverse problems in fields like NMR spectroscopy and geophysical tomography, highlighting the practical utility and theoretical underpinnings of least squares in real-world scenarios.

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