Improving the solvability of ill-conditioned systems of linear equations by reducing their condition numbers of their matrices

by Abdul Salam Mahama

Institution: Kwame Nkrumah University of Science and Technology
Year: 2016
Posted: 02/05/2017
Record ID: 2063593
Full text PDF: http://dspace.knust.edu.gh:8080/jspui/handle/123456789/8426


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. 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, 2015 KNUST