Numerical techniques in mathematical programming

[摘要] The application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency. Part A describes computation and updating of the product-form of the LU decomposition of a matrix and shows it can be applied to solving linear systems at least as efficiently as standard techniques using the product-form of the inverse. Part B discusses orthogonalization via Householder transformations, with applications to least squares and quadratic programming algorithms based on the principal pivoting method of Cottle and Dantzig. Part C applies the singular value decomposition to the nonlinear least squares problem and discusses related eigenvalue problems.

[学科分类] 计算机科学（综合）