“The object of investigation in this study is that of ill-conditioning in the solution of a system of linear equations. Ill-conditioning arises when the solution is very sensitive to small changes in the coefficients of the unknowns.
A study is made in this paper of the various proposed measures of ill-conditioning for the purpose of finding the most practical method or measure for determining whether a system is ill-conditioned.
The problem of near-singular or ill-conditioned systems is of great importance in the solution of linear systems because of the extensive use made of them in practical situations. Solution of a system of linear equations with this property frequently finds use in many areas of Applied Science. In applied mathematics, systems of linear equations are used in solving such problems as method of least squares, solution of partial differential equations, ordinary differential equations and many others.
Although computation of such a system could be done by double precision, giving increased accuracy at each step, this does not eliminate the problem. The problem of obtaining accurate data may be more important than the actual computation. However, when a system is found to be ill- conditioned, a method of higher precision is often used to improve round-off errors which would invalidate the solution. Nevertheless, it is the identification or means of detecting such a system which needs to be considered before further analysis can be pursued. In small systems the detection of ill-conditioning is fairly obvious by observation; whereas for larger systems, it is hidden from observation in most cases. Thus, an indicative measure is needed to detect such a system.
It is the aim of the author in this study to find a suitable measure or method for detecting an ill-conditioned system of equations”--Introduction, pages 1-2.
Lee, Ralph E., 1921-2010
Johnson, Charles A.
Fuller, Harold Q., 1907-1996
Miles, Aaron J.
Mathematics and Statistics
M.S. in Applied Mathematics
Missouri School of Mines and Metallurgy
v, 40 pages
© 1963 Thomas D. Calton, All rights reserved.
Thesis - Open Access
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Calton, Thomas D., "Investigation of measures of ill-conditioning" (1963). Masters Theses. 2839.