Progress in Numerical Analysis

Developments in numerical analysis fall into two separate categories. The first comprises work on problems which are unsolved in the sense that either no feasible methods are available or else there is no reliable analysis for the methods which are in use. The second category comprises work on solved problems and its aim is to remove the human user from the solution process, in so far as this is possible, and also to improve efficiency in regard to other factors such as execution time, storage requirements or length of code.Shortly after the introduction of modern digital computers and high level programming languages most of numerical analysis fell into the unsolved category. With every success in this category the second one has grown–and vice versa. In order to judge properly the value of the multifarious research activities in numerical analysis it is important to grasp the evolution of this sprawling empire.In this essay we point out some muddles caused by not discriminating between the two categorie...

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