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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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IV.21 Numerical Analysis

Lloyd N. Trefethen

1 The Need for Numerical Computation

Everyone knows that when scientists and engineers need numerical answers to mathematical problems, they turn to computers. Nevertheless, there is a widespread misconception about this process.

The power of numbers has been extraordinary. It is often noted that the scientific revolution was set in motion when Galileo and others made it a principle that everything must be measured. Numerical measurements led to physical laws expressed mathematically, and, in the remarkable cycle whose fruits are all around us, finer measurements led to refined laws, which in turn led to better technology and still finer measurements. The day has long since passed when an advance ...

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