Digital Commons Network^™

Comparative Analysis Of Numerical Integration Techniques, Edward Lee Sartore

Masters Theses

"When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson's rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by √1-x ², or as a function g(x) times (1-x)^α (l+x)^ß , where α and ß are some real numbers >1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and …

A Study Of The Development Of A Heuristic Program That Solves Symbolic Laplace Transformation Problems, Arthur E. Zackrison

Masters Theses

"A medium-speed general purpose digital computer (IBM 1620 Model II) was programmed to solve symbolic Laplace transformation problems. Although the applied mathematician and modern engineer has many uses for the symbolic solution of a problem, the potential of symbolic manipulation by a computer has not yet been sufficiently developed to help them because of many problems. This paper discusses the program and based on the author’s experience with it’s [sic] performance, clarifies the position of several of these difficulties and reaches some conclusions concerning computer solution of such problems"--Abstract, page ii.

Error Analysis Of Rational Approximations Of Functions With Emphasis On Minimax Techniques, Mary Frances Good

Masters Theses

"This study examines the various considerations which are made when a function is approximated by a rational function. None of the four approximations considered here gives both a rapidly calculated approximation and one in which the maximum magnitude of the error function over a given interval is a minimum.

The second algorithm of Remes produces a sequence of rational approximations which converge to the rational approximation that minimizes the maximum magnitude of the error function for a given number of parameters to be calculated if the initial approximation in the sequence is chosen properly. Several rational function approximations are investigated …

Stable Predictor-Corrector Methods For First Order Ordinary Differential Equations, Terrell Lester Carlson

Masters Theses

"Because of the wide variety of differential equations, there seems to be no numerical method which will affect the solution best for all problems. Predictor-corrector methods have been developed which utilize more ordinates in the predictor and corrector equations in the search for a better method.

These methods are compared for stability and convergence with the well known methods of Milne, Adams, and Hamming"--Abstract, page ii.

A Comparison Of The Lr And Qr Transformations For Finding The Eigenvalues For Real Nonsymmetric Matrices, Susan Clara Hanson

Masters Theses

"The LR and QR algorithms, two of the best available iterative methods for finding the eigenvalues of a nonsymmetric matrix associated with a system of linear homogeneous equations, are studied. These algorithms are discussed as they apply to the determination of the eigenvalues of real nonsymmetric matrices.

A comparison of the speed and accuracy of these transformations is made. A detailed discussion of the criterion for convergence and the numerical difficulties which may occur in the computation of multiple and complex conjugate eigenvalues are included.

The results of this study indicate that the QR algorithm is the more successful method …

A Simulation Study Of A Proposed Computer Installation, John Edward Hawthorne

Masters Theses

"The operation of a data processing center has been studied with the objective of investigating the effect of various facilities, job loads, and operating policies as measured by job turnaround time. The mechanism for study was digital computer simulation.

This thesis purports to review the technology of simulation and the associated computer techniques, defines the problem and the alternatives available, and analyzes the results derived from the experiments.

Conclusions drawn from this study support the current practice of a functioning data processing center"--Abstract, page ii.