Least Squares Methods in Physics and Engineering

摘要

These lectures deal with numerical methods representing the state of the art, including the available computer software. First a brief background of basic matrix factorizations is given. Dense linear problems are then treated, including methods for updating the solution when rows and variables are added or deleted. Special consideration is given to weighted least squares problems and constrained problems. Regularization of ill-posed problems are briefly surveyed. Sparse linear least squares problems are treated in some detail. Different ordering schemes, including ordering to block-angular form and nested dissection, and iterative methods are discussed. Finally a survey of methods for nonlinear least squares problems is given. The Gauss-Newton method is analyzed and its local convergence derived. Levenberg-Marquardt methods are discussed and different methods using second derivative information surveyed. Special methods are given for separable linear-nonlinear problems. (Atomindex citation 13:676172)