Editing Numerical analysis (section)

==Software==
{{Main|List of numerical-analysis software|Comparison of numerical-analysis software}}

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]].

Over the years the [[Royal Statistical Society]] published numerous algorithms in its [[Journal of the Royal Statistical Society, Series C (Applied Statistics)|''Applied Statistics'']] (code for these "AS" functions is [https://jblevins.org/mirror/amiller/#apstat here]); 
[[Association for Computing Machinery|ACM]] similarly, in its ''[[Transactions on Mathematical Software]]'' ("TOMS" code is [https://jblevins.org/mirror/amiller/#toms here]).
The [[Naval Surface Warfare Center]] several times published its [https://apps.dtic.mil/sti/pdfs/ADA476840.pdf ''Library of Mathematics Subroutines''] (code [https://jblevins.org/mirror/amiller/#nswc here]).

There are several popular numerical computing applications such as [[MATLAB]],<ref>{{cite book |last1=Quarteroni |first1=A. |last2=Saleri |first2=F. |last3=Gervasio |first3=P. |title=Scientific computing with MATLAB and Octave |publisher=Springer |edition=4th |date=2014 |isbn=978-3-642-45367-0 |url={{GBurl|_0m9BAAAQBAJ|pg=PR11}}}}</ref><ref name="gh">{{cite book |editor1-last=Gander |editor1-first=W. |editor2-last=Hrebicek |editor2-first=J. |title=Solving problems in scientific computing using Maple and Matlab® |publisher=Springer |date=2011 |isbn=978-3-642-18873-2 |url={{GBurl|di2qCAAAQBAJ|pg=PR14}}}}</ref><ref name="bf">{{cite book |last1=Barnes |first1=B. |last2=Fulford |first2=G.R. |title=Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB |publisher=CRC Press  |edition=2nd |date=2011 |isbn=978-1-4200-8350-7 |oclc=1058138488 }}</ref> [[TK Solver]], [[S-PLUS]], and [[IDL (programming language)|IDL]]<ref>{{cite book |first=L.E. |last=Gumley |title=Practical IDL programming |publisher=Elsevier |date=2001 |isbn=978-0-08-051444-4 |url={{GBurl|1d-tNpm_x4gC|pg=PR9}}}}</ref> as well as free and open-source alternatives such as [[FreeMat]], [[Scilab]],<ref>{{cite book |last1=Bunks |first1=C. |last2=Chancelier |first2=J.P. |last3=Delebecque |first3=F. |last4=Goursat |first4=M. |last5=Nikoukhah |first5=R. |last6=Steer |first6=S. |title=Engineering and scientific computing with Scilab |publisher=Springer |date=2012 |isbn=978-1-4612-7204-5 }}</ref><ref>{{cite book |last1=Thanki |first1=R.M. |last2=Kothari |first2=A.M. |title=Digital image processing using SCILAB |publisher=Springer |date=2019 |isbn=978-3-319-89533-8 |url={{GBurl|VydaDwAAQBAJ|pg=PR9}}}}</ref> [[GNU Octave]] (similar to Matlab), and [[IT++]] (a C++ library). There are also programming languages such as [[R (programming language)|R]]<ref>{{cite journal |last1=Ihaka |first1=R. |last2=Gentleman |first2=R. |title=R: a language for data analysis and graphics |journal=Journal of Computational and Graphical Statistics |volume=5 |issue=3 |pages=299–314 |date=1996 |doi=10.1080/10618600.1996.10474713 |s2cid=60206680 |url=https://www.stat.auckland.ac.nz/~ihaka/downloads/R-paper.pdf}}</ref> (similar to S-PLUS), [[Julia (programming language)|Julia]],<ref>{{Cite journal|last1=Bezanson|first1=Jeff|last2=Edelman|first2=Alan|last3=Karpinski|first3=Stefan|last4=Shah|first4=Viral B.|date=2017-01-01|title=Julia: A Fresh Approach to Numerical Computing|url=https://epubs.siam.org/doi/abs/10.1137/141000671|journal=SIAM Review|volume=59|issue=1|pages=65–98|doi=10.1137/141000671|arxiv=1411.1607 |issn=0036-1445|hdl=1721.1/110125|s2cid=13026838 |hdl-access=free}}</ref> and [[Python (programming language)|Python]] with libraries such as [[NumPy]], [[SciPy]]<ref>Jones, E., Oliphant, T., & Peterson, P. (2001). SciPy: Open source scientific tools for Python.</ref><ref>{{cite book |first=E. |last=Bressert |title=SciPy and NumPy: an overview for developers |publisher=O'Reilly |date=2012 |isbn=9781306810395 }}</ref><ref>{{cite book |first=F.J. |last=Blanco-Silva |title=Learning SciPy for numerical and scientific computing |publisher=Packt |date=2013 |isbn=9781782161639 }}</ref> and [[SymPy]]. Performance varies widely: while vector and matrix operations are usually fast, scalar loops may vary in speed by more than an order of magnitude.<ref>[http://www.sciviews.org/benchmark/ Speed comparison of various number crunching packages] {{webarchive |url=https://web.archive.org/web/20061005024002/http://www.sciviews.org/benchmark/ |date=5 October 2006 }}</ref><ref>[http://www.scientificweb.com/ncrunch/ncrunch5.pdf Comparison of mathematical programs for data analysis] {{Webarchive|url=http://arquivo.pt/wayback/20160518062220/http://www.scientificweb.com/ncrunch/ncrunch5.pdf |date=18 May 2016 }} Stefan Steinhaus, ScientificWeb.com</ref>

Many [[computer algebra system]]s such as [[Mathematica]] also benefit from the availability of [[arbitrary-precision arithmetic]] which can provide more accurate results.<ref>{{cite book |first=R.E. |last=Maeder |title=Programming in mathematica |publisher=Addison-Wesley |edition=3rd |date=1997 |isbn=9780201854497 |oclc=1311056676 |url=https://archive.org/details/programminginmat0000maed_l2m6}}</ref><ref>{{cite book |first=Stephen |last=Wolfram |date=1999 |title=The MATHEMATICA® book, version 4 |publisher=[[Cambridge University Press]] |url={{GBurl|Xny77v_QPkEC|pg=PR19}} |isbn=9781579550042 }}</ref><ref>{{cite book |last1=Shaw |first1=W.T. |last2=Tigg |first2=J.  |title=Applied Mathematica: getting started, getting it done |publisher=Addison-Wesley |date=1993 |isbn=978-0-201-54217-2 |oclc=28149048 |url=http://www.gbv.de/dms/bowker/toc/9780201542172.pdf}}</ref><ref>{{cite book |last1=Marasco |first1=A. |last2=Romano |first2=A. |title=Scientific Computing with Mathematica: Mathematical Problems for Ordinary Differential Equations |publisher=Springer |date=2001 |isbn=978-0-8176-4205-1 |url={{GBurl|iFRqemnmMqUC|pg=PR7}}}}</ref>

Also, any [[spreadsheet]] [[software]] can be used to solve simple problems relating to numerical analysis. 
[[Microsoft_Excel#|Excel]], for example, has hundreds of [[Microsoft Excel#Functions|available functions]], including for matrices, which may be used in conjunction with its [[Microsoft Excel#Add-ins|built in "solver"]].