Regularization of Ill-Conditioned Linear Systems - Sheima M. E. Abueldahab

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Résumé :
Ill-conditioned linear systems arise in many applications, for example, in the solution of integral equations, and in the solution of non-linear programming problems. In many application of linear algebra, the need arises to find a good approximation matrix (bx) to a vector (x) satisfying an approximating equation Ax ? b with ill-conditioned matrix (A) , given matrix (b). Straightforward the computed solution (bx) is usually meaningless approximation to ( x ) due to the error in the righthand side ( b ) and the severe ill-conditioning of the matrix ( A).In order to avoid this difficulty, one typically replaces the linear systems Ax = b, by a nearby system that is less sensitive to the error in (b) and considers the computed solution of the latter system an approximation of (x). This replacement is known as regularization. This work examines various regularization methods for computing stable solution to ill-conditioned linear systems....

Biographie:
I am a lecturer at the faculty of Engineering, University of Khartoum. In 2002 I held the BSc, first honor degree in Mathematics from the univ. of Khartoum. In 2006 I held the MSc in Industerial and Comutational Mathematics science from univ. of Khartoum. In 2007 I held the post graduate diploma in Mathematics from the Western Cape university....