Numerical Analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection (YBC 7289), which gives a sexagesimal numerical approximation of, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in carpentry and construction.

Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.

Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in the movement of heavenly bodies (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

Before the advent of modern computers numerical methods often depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead. These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.

Read more about Numerical AnalysisGeneral Introduction, Generation and Propagation of Errors, Areas of Study, Software

Other articles related to "numerical analysis, numerical, analysis":

Numerical Analysis - Software
... The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C ... Commercial products implementing many different numerical algorithms include the IMSL and NAG libraries a free alternative is the GNU Scientific Library ... There are several popular numerical computing applications such as MATLAB, S-PLUS, LabVIEW, and IDL as well as free and open source alternatives such as FreeMat, Scilab, GNU Octave (similar ...
Leslie Fox
... mathematician noted for his contribution to numerical analysis ... He worked on the numerical solution of partial differential equations at a time when numerical linear algebra was performed on a desk calculator ... In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford ...
Fields of Mathematics - Applied Mathematics - Computational Mathematics
... problems that are typically too large for human numerical capacity ... Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory numerical analysis includes the study of ... Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic matrix and graph theory ...
Gaetano Fichera - Work - Research Activity - Numerical Analysis
... As noted in the "Functional analysis and eigenvalue theory" section, his main direct contribution to the field of numerical analysis is the introduction ... paper (Fichera 1975), which deals with the asymptotic analysis of the potential, were included in the book (Fichera 1978a) and led to the definition of the ... study (Fichera, Sneider Wyman 1977), surveyed in (Fichera 1978b), where methods of mathematical analysis and numerical analysis are applied to a problem posed by biological sciences ...
Leslie Fox - Fox's Wider Influence
... While Fox influenced the development of numerical analysis through his undergraduate teaching and postgraduate supervision (he supervised around 19 doctoral students ... answers', describing some of the pitfalls of numerical computation from the uncritical use of simple methods Fox played a signifficant part in the early days ... as an editor first of the main 'IMA Journal and later the specialised Journal of Numerical Analysis, started in 1981 ...

Famous quotes containing the words analysis and/or numerical:

    Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.
    Joan Didion (b. 1934)

    The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.
    Ralph Waldo Emerson (1803–1882)