Improving the solvability of ill-conditioned systems of linear equations by reducing their condition numbers of their matrices.
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Date
October 12, 2015
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Abstract
This thesis is concerned with the solution of a canonical example of ill-conditioned
system called Hilbert Systems of Linear Equations (HSLE's) via the solution of
an equivalent/transformed HSLE's which are well-conditioned. A matrix is rst
constructed from that of the given ill-conditioned system. Then, an adequate
right-hand side is computed to make up the instance of an equivalent system.
Formulae and algorithms for computing an instance of this equivalent HSLE and
solving it will be given and illustrated. Analysis is made between the original
Hilbert system and its equivalent/transformed system. Under original Hilbert
system comparison is made between unperturbed and perturbed Hilbert system
and under the equivalent/transformed Hilbert system comparison is made be-
tween unperturbed and perturbed transformed Hilbert system. The results es-
tablished the fact that well conditioned solutions are more accurate and reliable
than ill conditioned solutions due to their error margins and condition numbers.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree
of Master of Science in Industrial Mathematics.