Statistics and Probability Commons^™

Design Optimization Using Model Estimation Programming, Richard Kay Brimhall

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.

Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for …

Fortran Programs For The Calculation Of Most Of The Commonly Used Experimental Design Models, H. Wain Greenhalgh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two computer programs were developed using a CDC 3100. They were written in FORTRAN IV.

One program uses four tape drives, one card reader, and one printer. It will calculate factorial analysis of variance with or without covariance and/or multivariate analysis for one to eight factors and up to twenty-five variables.

The other program is used for completely randomized designs, randomized block designs, and latin square designs. It will handle twenty-five treatments, rows (blocks), and columns. The program can handle fifteen variables using any number of these variables for covariates.

Rational Arithmetic As A Means Of Matrix Inversion, Jay Roland Peterson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The solution to a set of simultaneous equations is of the form A^-1 B = X where A^-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A^-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations.

This study describes a matrix inversion program written in SPS II, utilizing the concept of rational arithmetic. This program, using the Gaussian elimination matrix inversion method, is compared to the same method written in Fortran. Gaussian elimination …