1. A question of "roundness

With the advent of the first computers, and thanks to their high computing speed, problems that once required a large number of arithmetic operations could now be solved. But users were already asking themselves: "At the end of a long sequence of calculations on a computer, because of the propagation of rounding errors, is the result obtained significant?"

In 1946, Von Neumann performed turbulence calculations on the IBM SSEC (Selective Sequence Electronic Calculator) computer. This was a failure due to the propagation of round-off errors. He concluded that the computer could never be used for scientific computing.

But later work (Von Neumann and Goldstine, 1947) on calculating the inverse of a positive-definite matrix using Gauss's method showed that the propagation of round-off errors was not as catastrophic as had been feared. This reassured...