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Don't fucking piss me off. DPMO. Don't mess with me. who in their right mind decided to add an llm generatedsummary that does nothing but clog the article up |
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'''Numerical analysis''' is the study of [[algorithm]]s that use numerical [[approximation]] (as opposed to [[symbolic computation|symbolic manipulations]]) for the problems of [[mathematical analysis]] (as distinguished from [[discrete mathematics]]). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: [[ordinary differential equation]]s as found in [[celestial mechanics]] (predicting the motions of planets, stars and galaxies), [[numerical linear algebra]] in data analysis,<ref>{{cite book |first=J.W. |last=Demmel |title=Applied numerical linear algebra |publisher=[[Society for Industrial and Applied Mathematics|SIAM]] |date=1997 |isbn=978-1-61197-144-6 |doi=10.1137/1.9781611971446 |url=https://epubs.siam.org/doi/epdf/10.1137/1.9781611971446.fm}}</ref><ref>{{cite book |last1=Ciarlet |first1=P.G. |last2=Miara |first2=B. |last3=Thomas |first3=J.M. |title=Introduction to numerical linear algebra and optimization |publisher=Cambridge University Press |date=1989 |isbn=9780521327886 |oclc=877155729 }}</ref><ref>{{cite book |last1=Trefethen |first1=Lloyd |last2=Bau III |first2=David |title=Numerical Linear Algebra |publisher=SIAM |date=1997 |isbn=978-0-89871-361-9 |url={{GBurl|4Mou5YpRD_kC|pg=PR7}}}}</ref> and [[stochastic differential equation]]s and [[Markov chain]]s for simulating living cells in medicine and biology.
Before modern computers, [[numerical method]]s often relied on hand [[interpolation]] formulas, using data from large printed tables. Since the mid
The numerical point of view goes back to the earliest mathematical writings. A tablet from the [[Yale Babylonian Collection]] ([[YBC 7289]]), gives a [[sexagesimal]] numerical approximation of the [[square root of 2]], the length of the [[diagonal]] in a [[unit square]].
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==Software==
{{Main|List of numerical-analysis software|Comparison of numerical-analysis software|List of programming languages by type#Numerical analysis|l3=Numerical analysis programming languages|List of numerical libraries}}
Since the late twentieth century, most algorithms are implemented in a variety of programming languages. The [[Netlib]] repository contains various collections of software routines for numerical problems, mostly in [[Fortran]] and [[C (programming language)|C]]. Commercial products implementing many different numerical algorithms include the [[IMSL Numerical Libraries|IMSL]] and [[Numerical Algorithms Group|NAG]] libraries; a [[free software|free-software]] alternative is the [[GNU Scientific Library]].
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*[[:Category:Numerical analysts]]
*[[Analysis of algorithms]]
*[[Approximation theory]]
*[[Computational science]]
*[[Computational physics]]
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*[https://dlmf.nist.gov/3 Numerical Methods], ch 3. in the ''[[Digital Library of Mathematical Functions]]''
*[https://personal.math.ubc.ca/~cbm/aands/page_875.htm Numerical Interpolation, Differentiation and Integration], ch 25. in the ''Handbook of Mathematical Functions'' ([[Abramowitz and Stegun]])
*[https://fncbook.com/ Tobin A. Driscoll and Richard J. Braun: ''Fundamentals of Numerical Computation'' (free online version)]
===Online course material===
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