Grafarend E.W. Linear and Nonlinear Models: Fixed Effects, Random Effects, and Mixed Models

Walter de Gruyter, 2006. — 752 p. — ISBN: 3110162164, 978-3110162165.This monograph offers a thorough treatment of methods for solving over- and underdetermined systems of equations. The considered problems can be non-linear or linear, and deterministic models as well as statistical effects are discussed. Considered methods include, e.g., minimum norm and least squares solution methods with respect to weighted norms. In-addition, minimum bias and minimum variance methods as well as the Tikhonov-Phillips regularization are considered. In an extensive appendix, all necessary prerequisites like matrix algebra, matrix analysis and Lagrange multipliers are presented. An extended list of references is also provided.