# The Definition of Numerical Analysis - 1992

## Details

Title : The Definition of Numerical Analysis Author(s): Trefethen, L. Link(s) : https://www.semanticscholar.org/paper/The-Definition-of-Numerical-Analysis-Trefethen/d78e9fc13dcddd9e20b0c2e398de1887d68ac6ed

## Rough Notes

Author starts with a wrong definition: "Numerical analysis is the study of rounding errors" - he argues that rounding errors are not fundamental. He is convinced that many think this definition is half-true. Even if rounding errors are eliminated, numerical analysis will still exist since closed form solutions do not exist for many problems (e.g. finding roots of polynomials with degree more than 4).

Regarding Singular Value Decomposition (SVD), author states that Gene Golub and other numerical analysts made it prominent in the 1960's although it existed long before that.

Author's proposed new definition is: "Numerical analysis is the study of algorithms for the problems of continuous mathematics". Here, **algorithms** is a key word.

"If Euler were alive today, he would not be proving existence theorems".