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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to numerical analysis: the study of methods of computing numerical data. In many problems this implies producing a sequence of approximations; thus the questions involve the rate of convergence, the accuracy (or even validity) of the answer, and the completeness of the response. Since many problems across mathematics can be reduced to linear algebra, this too is studied numerically; here there are significant problems with the amount of time necessary to process the initial data. Numerical solutions to differential equations require the determination not of a few numbers but of an entire function; in particular, convergence must be judged by some global criterion. Other topics include numerical simulation, optimization, and graphical analysis, and the development of robust working code. Numerical linear algebra topics: solutions of linear systems AX = B, eigenvalues and eigenvectors, matrix factorizations. Calculus topics: numerical differentiation and integration, interpolation, solutions of nonlinear equations f(x) = 0. Statistical topics: polynomial approximation, curve fitting. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
|Math Topics:||Numerical Analysis|
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