Effective Numerical Methods and Average Errors
The final aim of numerical analysis is the construction and identification of effective numerical methods. Generally spoken, an effective method should be stable in a certain sense and also its error should be small compared to its computational cost. We do not discuss stability here and of course we do not have a definition of an ‘effective method’ that could always be applied. We only have several notions of the error and the cost of a method on one side and some heuristic ideas acquired by many numerical calculations on the other side.
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