The effect of television on the leisure time activities of sixth grade children in Medford, Massachusetts.

Thesis (Ed.M.)--Boston Universit

A New Approximation of the Schur Complement in Preconditioners for PDE Constrained Optimization

Saddle point systems arise widely in optimization problems with constraints. The utility of Schur complement approximation is now broadly appreciated in the context of solving such saddle point systems by iteration. In this short manuscript, we present a new Schur complement approximation for PDE constrained optimization, an important class of these problems. Block diagonal and block triangular preconditioners have previously been designed to be used to solve such problems along with MINRES and non-standard Conjugate Gradients respectively; with appropriate approximation blocks these can be optimal in the sense that the time required for solution scales linearly with the problem size, however small the mesh size we use. In this paper, we extend this work to designing such preconditioners for which this optimality property holds independently of both the mesh size and of the Tikhonov regularization parameter \beta that is used. This also leads to an effective symmetric indefinite preconditioner that exhibits mesh and \beta-independence. We motivate the choice of these preconditioners based on observations about approximating the Schur complement obtained from the matrix system, derive eigenvalue bounds which verify the effectiveness of the approximation, and present numerical results which show that these new preconditioners work well in practice

Fast iterative solvers for convection-diffusion control problems

In this manuscript, we describe effective solvers for the optimal control of stabilized convection-diffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretize-then-optimize or optimize-then-discretize approach for this problem is used. We then derive two effective preconditioners for this problem, the �first to be used with MINRES and the second to be used with the Bramble-Pasciak Conjugate Gradient method. The key components of both preconditioners are an accurate mass matrix approximation, a good approximation of the Schur complement, and an appropriate multigrid process to enact this latter approximation. We present numerical results to demonstrate that these preconditioners result in convergence in a small number of iterations, which is robust with respect to the mesh size h, and the regularization parameter β, for a range of problems

Resistant And Susceptible BIB Designs

Statistic

Program and abstracts for the 11th annual Tropical and Subtropical Fisheries Technological Conference of the Americas, January 13 - 16, 1986, Holiday Inn, International Airport, Tampa, Florida

The Tropical and Subtropical Fisheries Technological Society of the Americas is a professional , educational association of fishery techno1ogists interested in the application of science to the unique problems of production, processing, packaging, distribution and utilization of tropical and subtropical fishery species. Individual abstracts edited by the authors of the abstracts. Some abstracts have been excluded by author request. (26pp.

Accuracy and Precision of Insect Density and Impact Estimates

In estimating insect density and impact, entomologists are understandably interested in accuracy of estimation, but they almost always are dealing with precision because of bias due to an invalid estimator, probability sampling, or nonsampling errors. Definitions related to statistical estimation are reviewed and the concepts of accuracy and precision examined. Interval estimation and optimum sample size determination related to accuracy and precision, using the concept of allowable error, are examined. Criteria for selecting the best estimator in tenns of accuracy and precision are presented, and the distortion of probability statements due to bias is discussed. Accuracy and precision are compared and contrasted using two examples: (I) estimating insect density and (2) estimating insect impact. Adjusted and more accurate estimators can be obtained if the bias of an estimator can be estimated from a preliminary sample