\( \newcommand\D{\mathrm{d}} \newcommand\E{\mathrm{e}} \newcommand\I{\mathrm{i}} \newcommand\bigOh{\mathcal{O}} \newcommand{\cat}[1]{\mathbf{#1}} \newcommand\curl{\vec{\nabla}\times} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\RR}{\mathbb{R}} \newcommand{\ZZ}{\mathbb{Z}} \)
UP | HOME

Numerical Analysis

Numerical analysis is the study of algorithms for solving the problems of continuous mathematics, by which we mean problems involving real or complex variables. (This definition includes problems like linear programming and the traveling salesman problem posed over the real numbers, but not their discrete analogues.)

— Lloyd N. Trefethen, "Numerical Analysis" in Princeton Companion of Mathematics (2006)

The basic outline of the subject, as presented in most textbooks, first presents floating-point arithmetic, then root finding algorithms, polynomial interpolation, quadrature, numerical linear algebra, then using the numerical linear algebra to solve differential equations. Once all this has been established, various other ways to solve differential equations are discussed in graduate courses or their own texts.

(Note: Most of what I've written can be found in my notes on numerical analysis, with implementations in Fortran.)

Last Updated 2022-04-11 Mon 08:45.