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This thesis deals with four important matrix problems: the application of many variants of the conjugate gradient method for solving matrix equations, the solution of lower and upper bounds guadratic programs associated with M-matrices, the construction of a Block Lanczos method for computing the greatest singular values of a matrix, and the computation of the singular value decomposition of a matrix on the ILLIAC-IV computer. (Author).

The central server model is used to extend Buzen's results on balance and bottlenecks. Two measures are developed which appear to be useful for evaluating and improving computer system performance. The first measure, called the balance index, is useful for balancing requests to the peripheral processors. The second quantity, called the sensitivity index, indicates which processing rates have the most effect on overall system performance.

A flow table model is defined for parallel computer systems. In the model, fundamental-mode flow tables are used to describe the operation of system components, which may be programs or circuits. Components communicate by changing the values on interconnecting lines which carry binary level signals. It is assumed that there is no bound on the time for value changes to propagate over the interconnecting lines. Given this delay assumption, it is necessary to specify a mode of operation for system components such that input changes which arrive while a component is unstable do not affect the operation of the component. Such a mode of operation is specified. Using the flow table model, a new control algorithm for the two-process mutual exclusion problem is designed. This algorithm does not depend on the exclusive execution of any primitive operations used in its implementation. A circuit implementation of the control algorithm is described. (Author).

This dissertation is concerned with the development and numerical implementation of algorithms for solving finite dimensional optimization problems. Special emphasis is given to robustness, by which is meant the ability of an algorithm to cope with adverse circumstances, whether due to pathologies of a particular problem or to the shortcomings of finite precision computer arithmetic. A uniform framework is developed in which a common set of techniques may be applied to all of the standard problems of optimization. The algorithms are based on Newton-like methods implemented in a robust manner by means of hybrid, curved line searches and stable linear algebra techniques. Developed first in the context of systems of nonlinear equations, nonlinear least squares, and unconstrained minimization, the algorithms are combined and extended to include problems with equality or inequality constraints. Constrained problems are handled by means of separate line searches in the range and null spaces of the matrix of constraint normals. The classical Lagrangian is modified to allow the same Newton-like methods to be applied to inequality constraints. Test results are presented which show the validity and promise of the methods developed in this dissertation. (Author).

Abstract: "The linear program min c[superscript T]x subject to Ax=b, x [greater than or equal to] 0, is solved by the projected Newton barrier method. The method consists of solving a sequence of subproblems of the form [formula] subject to Ax=b. Extensions for upper bounds, free and fixed variables are given. A linear modification is made to the logarithmic barrier function, which results in the solution being bounded in all cases. It also facilitates the provision of a good starting point. The solution of each subproblem involves repeatedly computing a search direction and taking a step along this direction. Ways to find an initial feasible solution, step sizes and convergence criteria are discussed.

The Meta-DENDRAL program is a vehicle for studying problems of theory formation in science. The general strategy of Meta-DENDRAL is to reason from data to plausible generalizations and then to organize the generalizations into a unified theory. Three main subproblems are discussed: Explain the experimental data for each individual chemical structure; Generalize the results from each structure to all structures; Organize the generalizations into a unified theory. The program is built upon the concepts and programmed routines already available in the Heuristic DENDRAL performance program, but goes beyond the performance program in attempting to formulate the theory which the performance program will use. (Author).