Manuscript of Stiefel‘s 1949 course on numerical methods
If one solves numerical problems with machines, then  the methods are mostly very different to those of manual computing and the adaptation of mathematical methods to the machine has become a young new branch of math, which gets in the USA its first cultivation. One point I want to make in advance: a computing method is suitable for the machine, if it consists of a very frequent repetition of a simple single step.
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Based on his experiences Stiefel did not share this opinion. Already at the start of his endeavors in numerical analysis he wrote in lecture notes the following: