Numerical Algorithm: Difference between revisions

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#REDIRECT [[Numerical Approximation Algorithm]]
A [[Numerical Algorithm]] is an [[Algorithm]] that ...
* <B>AKA:</B> [[Numerical Analysis]].
* <B>See:</B> [[Algorithm]], [[Approximation]], [[Symbolic Computation]], [[Mathematical Analysis]], [[Discrete Mathematics]], [[Yale Babylonian Collection]], [[Sexagesimal]], [[Numerical Approximation]], [[Diagonal]], [[Unit Square]], [[Astronomy]], [[Carpentry]], [[Ordinary Differential Equation]].
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==References==
 
=== 2014 ===
* (Wikipedia, 2014) &rArr; http://en.wikipedia.org/wiki/numerical_analysis Retrieved:2014-5-17.
** '''Numerical analysis''' is the study of [[algorithm]]s that use numerical [[approximation]] (as opposed to general [[symbolic computation|symbolic manipulations]]) for the problems of [[mathematical analysis]] (as distinguished from [[discrete mathematics]]). <P> One of the earliest mathematical writings is a Babylonian tablet from the [[Yale Babylonian Collection]] (YBC 7289), which gives a [[sexagesimal]] numerical [[numerical approximation|approximation]] of <math>\sqrt{2}</math>, 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 [[astronomy]], [[carpentry]] and construction. <ref> The New Zealand Qualification authority specifically mentions this skill in document 13004 version 2, dated 17 October 2003 titled [http://www.nzqa.govt.nz/nqfdocs/units/pdf/13004.pdf CARPENTRY THEORY: Demonstrate knowledge of setting out a building] </ref> <P> Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of <math>\sqrt{2}</math>, 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. <P> Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st&nbsp;century also the life sciences and even the arts have adopted elements of scientific computations. [[Ordinary differential equation]]s appear in [[celestial mechanics]] (planets, stars and galaxies); [[numerical linear algebra]] is important for data analysis; [[stochastic differential equation]]s and [[Markov chain]]s are essential in simulating living cells for medicine and biology. <P> 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]].
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