Abstract:
Iterative Methods for Solving Systems of Equations
It is well known that a wide class of problems, which arises in pure and applied sciences
can be studied in the unified frame work of the system of absolute value equations of the
type
Ax − x = b, A ∈ Rn×n , b ∈ R n .
Here x is the vector in R n with absolute values of components of x. In this thesis,
several iterative methods including the minimization technique, residual method and
homotopy perturbation method are suggested and analyzed. Convergence analysis of
these new iterative methods is considered under suitable conditions. Several special cases
are discussed. Numerical examples are given to illustrate the implementation and
efficiency of these methods. Comparison with other methods shows that these new
methods perform better.
A new class of complementarity problems, known as absolute complementarity problem
is introduced and investigated. Existence of a unique solution of the absolute
complementarity problem is proved. A generalized AOR method is proposed. The
convergence of GAOR method is studied. It is shown that the absolute complementarity
problem includes system of absolute value equations and related optimizations as special
cases
