Summary:
This diploma thesis considers about the study and examination of the numerical
methods in the linear ill condition systems. In the first chapter, some
mathematical tools, that we generally use, are introduced in an analytic way.
The second chapter starts with the definition of the linear system of
least squares as well as its’ geometrical meaning. In this section we
demonstrated the being and the uniqueness of the least squares’ solution on
overdetermined and underdetermined systems. As we continue, we make a statement
about this solution’s sensitivity and the disturbances it provokes to the data,
namely solution changes by causing disturbances to vector b and table A.
Moving on chapter three, we makeahonorable mention on the numerical
methods that solve the least squares problem. Analytically for the linear
systems overdetermined we examined the normal equalizations method, the QR
factorization method, the Householder methods as well as MGS method. Also, we
examined for the linearunderdetermined systems the QR method as far as the
repetitive systems.
On the fourth chapter is given the full presentation and illustration
of the linear ill condition systems’ normalization. Crucial role in this
normalization plays the discovery of the parameter λand the analysis of the
special prices. Finally, we examined and developed the extrapolation method as
much as the specific algorithm.
Keywords:
Least Squares System, Rational Extrapolation Procedures, Linear Least Squares Problem, Full Rank, Condition Number
