Many problems in science and engineering have their mathematical
formulation as an operator equation of the form F(x) = y, where F
is a linear or nonlinear operator between certain function spaces.
In practice, such equations are solved approximately using
numerical methods, as their exact solution may not be often
possible or may not be worth looking for due to physical
constraints. In such situation, it is desirable to know how the
so-called approximate solution approximates the exact solution, and
what would be the error involved in such procedures. The main focus
of the book is on the study of stably solving nonlinear ill posed
operator equations of the form F(x)=y, with monotone nonlinear
operator F in an infinite dimensional real Hilbert space X, that
is, F obeys the monotonicity property. It is assumed that the exact
data y is unknown and usually only noisy data are available.
Problems of this type arise in a number of applications. Since the
solution does not depend continuously on the data, the ill-posed
problem has to be regularized. We considered iterative methods
which converge to the unique solution of the method of Lavrentiev
regularization.
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