Abstract
In the present work a common basis of convergence analysis is given for a large class of iterative procedures which we call general approximation methods. The concept of strong uniqueness is seen to play a fundamental role. The broad range of applications of this proposed classification will be made clear by means of examples from various areas of numerical mathematics. Included in this classification are methods for solving systems of equations, the Remes algorithm, methods for nonlinear Chebyshev-approximation, the classical Newton method along with its variants such as Newton's method for partially ordered spaces and for degenerate tangent spaces. As an example of the latter the approximation with exponential sums having coalescing frequencies is discussed, that is the case where the tangent space is degenerate.
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