  We introduce and analyze a fast iterative method based on sequential Bregman
projections for nonlinear inverse problems in Banach spaces. The key idea, in
contrast to the standard Landweber method, is to use multiple search directions
per iteration in combination with a regulation of the step width in order to
reduce the total number of iterations. This method is suitable for both exact
and noisy data. In the latter case, we obtain a regularization method. An
algorithm with two search directions is used for the numerical identification
of a parameter in an elliptic boundary value problem.
