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dbpedia:Numerical_analysis	rdfs:label	"Numerieke wiskunde"@nl ,
		"Numerical analysis"@en ,
		"An\u00E1lisis num\u00E9rico"@es ,
		"\u6570\u5024\u89E3\u6790"@ja ,
		"Analyse num\u00E9rique"@fr ,
		"Numerikus anal\u00EDzis"@hu ,
		"Numeerinen analyysi"@fi ,
		"Analisi numerica"@it ,
		"Analiz\u0103 numeric\u0103"@ro ,
		"\u041E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430"@uk ,
		"Analiza numeryczna"@pl ,
		"Say\u0131sal y\u00F6ntemler"@tr ,
		"\u6570\u503C\u5206\u6790"@zh ,
		"An\u00E1lise num\u00E9rica"@pt ,
		"Numerische Mathematik"@de ;
	dbpprop:abstract	"Numerieke wiskunde is een deelgebied van de wiskunde waarin algoritmes voor problemen in de continue wiskunde bestudeerd worden (in tegenstelling tot discrete wiskunde). Dit betekent dat het vooral gaat over re\u00EBle of complexe variabelen, de oplossing van differentiaalvergelijkingen en andere vergelijkbare problemen die optreden in de natuurkunde en techniek."@nl ,
		"File:Ybc7289-bw. jpg Babylonian clay tablet YBC 7289(c. 1800\u20131600 BCE) with annotations. (Image by Bill Casselman) Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). One of the earliest mathematical writings is the Babylonian tablet YBC 7289, which gives a sexagesimal numerical approximation of &lt;math&gt;\\sqrt{2}&lt;/math&gt;, 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 to &lt;math&gt;\\sqrt{2}&lt;/math&gt;, modern numerical analysis does not seek exact answers, because exact answers are 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); optimization occurs in portfolio management; numerical linear algebra is essential to quantitative psychology; 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. The interpolation algorithms nevertheless may be used as part of the software for solving differential equations."@en ,
		"F\u00E1jl:Ybc7289-bw. jpg YBC 7289-es babiloni agyagt\u00E1bla(ie. 1800\u20131600) A numerikus anal\u00EDzis olyan algoritmusokkal foglalkozik, melyek folytonos (teh\u00E1t nem diszkr\u00E9t) matematikai feladatokat oldanak meg. Az egyik legr\u00E9gebbi matematikai \u00EDr\u00E1s az YBC 7289-es sz\u00E1m\u00FA Babil\u00F3niai agyagt\u00E1bla, amely 60-as sz\u00E1mrendszerben jegyezte le a &lt;math&gt;\\sqrt{2}&lt;/math&gt; numerikus k\u00F6zel\u00EDt\u00E9s\u00E9t, ami egy egys\u00E9g n\u00E9gyzet \u00E1tl\u00F3j\u00E1nak hossza. A numerikus anal\u00EDzis folytatja ezt a hossz\u00FA trad\u00EDci\u00F3t, de nem keres pontos megold\u00E1sokat, mert a gyakorlatban lehetetlen ilyeneket adni. A numerikus anal\u00EDzis k\u00F6zel\u00EDt\u0151 megold\u00E1sokra t\u00F6rekszik, de \u00FAgy, hogy bizonyos elfogadhat\u00F3 hibahat\u00E1ron bel\u00FCl maradjanak. Alkalmazz\u00E1k m\u00E9rn\u00F6ki tudom\u00E1nyokban \u00E9s a term\u00E9szettudom\u00E1nyok t\u00F6bb \u00E1g\u00E1ban. A numerikus anal\u00EDzis egyik \u00E1ga, a numerikus line\u00E1ris algebra n\u00E9lk\u00FCl\u00F6zhetetlen a kvantitat\u00EDv pszichol\u00F3gi\u00E1ban. A sz\u00E1m\u00EDt\u00F3g\u00E9pek elterjed\u00E9se el\u0151tt a numerikus sz\u00E1m\u00EDt\u00E1sokat k\u00E9zzel v\u00E9gezt\u00E9k, a huszadik sz\u00E1zad k\u00F6zep\u00E9t\u0151l azonban fokozatosan sz\u00E1m\u00EDt\u00F3g\u00E9pek v\u00E1ltott\u00E1k fel ezt a m\u00F3dszert."@hu ,
		"File:Ybc7289-bw. jpg Babylonian clay tablet YBC 7289(c. 1800\u20131600 BCE) with annotations. (Image by Bill Casselman)\u6570\u503C\u5206\u6790\uFF08numerical analysis\uFF09\uFF0C\u662F\u6570\u5B66\u7684\u4E00\u4E2A\u5206\u652F\uFF0C\u4EE5\u6570\u5B57\u8BA1\u7B97\u673A\u6C42\u89E3\u6570\u5B66\u95EE\u9898\u7684\u7406\u8BBA\u548C\u65B9\u6CD5\u4E3A\u7814\u7A76\u5BF9\u8C61\u3002 \u6578\u767E\u5E74\u524D\uFF0C\u4EBA\u985E\u5DF2\u7D93\u5C07\u6578\u5B78\u61C9\u7528\u5728\u5EFA\u7BC9\u3001\u6230\u722D\u3001\u6703\u8A08\uFF0C\u4EE5\u53CA\u8A31\u591A\u9818\u57DF\u4E4B\u4E0A\uFF0C\u6700\u65E9\u7684\u6578\u5B78\u5927\u7D04\u662F\u897F\u5143\u524D1800\u5E74\u5DF4\u6BD4\u502B\u4EBA\u6CE5\u677F\uFF08Babylonian tablet \uFF09\u4E0A\u7684\u8A08\u7B97\u5F0F\u5B50\u3002\u4F8B\u5982\u6240\u8B02\u7684\u52FE\u80A1\u6578\uFF08\u7562\u6C0F\u4E09\u5143\u6578\uFF09\uFF0C\uFF083, 4, 5\uFF09\uFF0C\u662F\u76F4\u89D2\u4E09\u89D2\u5F62\u7684\u4E09\u908A\u9577\u6BD4\uFF0C\u5728\u5DF4\u6BD4\u502B\u6CE5\u677F\u4E0A\u5DF2\u7D93\u767C\u73FE\u4E86&lt;math&gt;\\sqrt{2}&lt;/math&gt;\u958B\u6839\u865F\u7684\u8FD1\u4F3C\u503C\u3002 \u6578\u503C\u5206\u6790\u5728\u50B3\u7D71\u4E0A\u4E00\u76F4\u4E0D\u65B7\u7684\u5728\u6539\u9032\uFF0C\u56E0\u70BA\u50CF\u5DF4\u6BD4\u502B\u4EBA\u7684&lt;math&gt;\\sqrt{2}&lt;/math&gt;\u8FD1\u4F3C\u503C\uFF0C\u81F3\u4ECA\u4ECD\u7136\u662F\u8FD1\u4F3C\u503C\uFF0C\u5373\u4F7F\u7528\u96FB\u8166\u8A08\u7B97\u4E5F\u627E\u4E0D\u5230\u6700\u7CBE\u78BA\u7684\u503C."@zh ,
		"Say\u0131sal y\u00F6ntemler, elde bulunan nicel (say\u0131sal) ve/veya nitel(niteliksel) de\u011Ferler \u0131\u015F\u0131\u011F\u0131nda \u00FCretim, ula\u015F\u0131m, konu\u015Fland\u0131rma gibi faaliyetlerde en ak\u0131lc\u0131 ve verimli karar\u0131 verme bilim dal\u0131d\u0131r. \u00C7\u00F6z\u00FCm problemin \u00F6zelli\u011Fine ba\u011Fl\u0131 olsa da genel anlamda minimum (en az) ya da maksimumdan (en \u00E7ok) ziyade optimumdur (en iyi). Say\u0131sal y\u00F6ntemler en iyiye ula\u015Fma \u00E7abas\u0131nda bir\u00E7ok matematiksel, istatistiksel ve s\u0131n\u0131fland\u0131rma yollu y\u00F6ntem i\u00E7erir."@tr ,
		"Die numerische Mathematik, kurz Numerik genannt, besch\u00E4ftigt sich als Teilgebiet der Mathematik mit der Konstruktion und Analyse von Algorithmen f\u00FCr kontinuierliche mathematische Probleme. Hauptanwendung ist dabei die Berechnung von L\u00F6sungen mit Hilfe von Computern."@de ,
		"\u041E\u0431\u0447\u0438\u0301\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0301\u0442\u0438\u043A\u0430 \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0449\u043E \u0432\u043A\u043B\u044E\u0447\u0430\u0454 \u043A\u043E\u043B\u043E \u043F\u0438\u0442\u0430\u043D\u044C, \u0437\u0432'\u044F\u0437\u0430\u043D\u0438\u0445 \u0437 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u044F\u043C \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u044C \u0456 \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u0430\u043D\u043D\u044F\u043C \u043A\u043E\u043C\u043F'\u044E\u0442\u0435\u0440\u0456\u0432. \u0423 \u0431\u0456\u043B\u044C\u0448 \u0432\u0443\u0437\u044C\u043A\u043E\u043C\u0443 \u0440\u043E\u0437\u0443\u043C\u0456\u043D\u043D\u0456, \u043E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u2014 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\u0437\u0430\u043F\u0430\u043C'\u044F\u0442\u0430\u0442\u0438 \u0442\u0456\u043B\u044C\u043A\u0438 2 \u0440\u0456\u0437\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B, \u0442\u043E\u043C\u0443 \u0432\u0430\u0436\u043B\u0438\u0432\u0443 \u0440\u043E\u043B\u044C \u0432 \u043E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0456\u0439 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u0432\u0456\u0434\u0456\u0433\u0440\u0430\u044E\u0442\u044C \u043E\u0446\u0456\u043D\u043A\u0438 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u0456 \u0430\u043B\u0433\u043E\u0440\u0438\u0442\u043C\u0456\u0432 \u0456 \u0457\u0445\u043D\u044F \u0441\u0442\u0456\u0439\u043A\u0456\u0441\u0442\u044C \u0434\u043E \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u044C \u043C\u0430\u0448\u0438\u043D\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0443 \u043A\u043E\u043C\u043F'\u044E\u0442\u0435\u0440\u0456. \u0421\u0430\u043C\u0435 \u0442\u043E\u043C\u0443, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0434\u043B\u044F \u0440\u043E\u0437\u0432\u2019\u044F\u0437\u0443\u0432\u0430\u043D\u043D\u044F \u043B\u0456\u043D\u0456\u0439\u043D\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u0438\u0447\u043D\u0438\u0445 \u0440\u0456\u0432\u043D\u044F\u043D\u044C \u0434\u0443\u0436\u0435 \u0440\u0456\u0434\u043A\u043E \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0457 \u043C\u0430\u0442\u0440\u0438\u0446\u0456, \u0442\u043E\u043C\u0443 \u0449\u043E \u0446\u0435\u0439 \u043C\u0435\u0442\u043E\u0434 \u043C\u043E\u0436\u0435 \u043F\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0434\u043E \u043F\u043E\u043C\u0438\u043B\u043A\u043E\u0432\u043E\u0433\u043E \u0440\u043E\u0437\u0432\u2019\u044F\u0437\u0443\u0432\u0430\u043D\u043D\u044F \u0443 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0437 \u0441\u0438\u043D\u0433\u0443\u043B\u044F\u0440\u043D\u043E\u044E \u043C\u0430\u0442\u0440\u0438\u0446\u0435\u044E, \u0430 \u0434\u0443\u0436\u0435 \u0440\u043E\u0437\u043F\u043E\u0432\u0441\u044E\u0434\u0436\u0435\u043D\u0438\u0439 \u0443 \u043B\u0456\u043D\u0456\u0439\u043D\u0456\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u043C\u0435\u0442\u043E\u0434 \u0437\u0430\u0441\u043D\u043E\u0432\u0430\u043D\u0438\u0439 \u043D\u0430 \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u0456 \u0432\u0438\u0437\u043D\u0430\u0447\u043D\u0438\u043A\u0430 \u043C\u0430\u0442\u0440\u0438\u0446\u0456 \u0456 \u0457\u0457 \u0434\u043E\u043F\u043E\u0432\u043D\u0435\u043D\u043D\u044F \u0432\u0438\u043C\u0430\u0433\u0430\u0454 \u043D\u0430\u0431\u0430\u0433\u0430\u0442\u043E \u0431\u0456\u043B\u044C\u0448\u0435 \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u0447\u043D\u0438\u0445 \u043E\u043F\u0435\u0440\u0430\u0446\u0456\u0439, \u043D\u0456\u0436 \u0431\u0443\u0434\u044C-\u044F\u043A\u0438\u0439 \u0441\u0442\u0456\u0439\u043A\u0438\u0439 \u043C\u0435\u0442\u043E\u0434 \u0440\u043E\u0437\u0432\u2019\u044F\u0437\u0443\u0432\u0430\u043D\u043D\u044F \u043B\u0456\u043D\u0456\u0439\u043D\u043E\u0457 \u0441\u0438\u0441\u0442\u0435\u043C\u0438 \u0440\u0456\u0432\u043D\u044F\u043D\u044C."@uk ,
		"L\u2019analyse num\u00E9rique est une discipline des math\u00E9matiques. Elle s\u2019int\u00E9resse tant aux fondements th\u00E9oriques qu\u2019\u00E0 la mise en pratique des m\u00E9thodes permettant de r\u00E9soudre, par des calculs purement num\u00E9riques, des probl\u00E8mes d\u2019analyse math\u00E9matique. Plus formellement, l\u2019analyse num\u00E9rique est l\u2019\u00E9tude des algorithmes permettant de r\u00E9soudre les probl\u00E8mes de math\u00E9matiques continues. Cela signifie qu\u2019elle s\u2019occupe principalement de r\u00E9pondre num\u00E9riquement \u00E0 des questions \u00E0 variable r\u00E9elle ou complexe comme l\u2019alg\u00E8bre lin\u00E9aire num\u00E9rique sur les champs r\u00E9els ou complexes, la recherche de solution num\u00E9rique d\u2019\u00E9quations diff\u00E9rentielles et d\u2019autres probl\u00E8mes li\u00E9s survenant dans les sciences physiques et l\u2019ing\u00E9nierie. Sa mise en \u0153uvre pratique et ses domaines d\u2019application sont d\u00E9crits plus compl\u00E8tement dans l\u2019article calcul num\u00E9rique."@fr ,
		"\u30D5\u30A1\u30A4\u30EB:Ybc7289-bw. jpg \u30D0\u30D3\u30ED\u30CB\u30A2\u306E\u7C98\u571F\u677F YBC 7289 \uFF08\u7D00\u5143\u524D1800-1600\u5E74\u9803\uFF09 2\u306E\u5E73\u65B9\u6839\u306E\u8FD1\u4F3C\u5024\u306F60\u9032\u6CD5\u30674\u6841\u300110\u9032\u6CD5\u3067\u306F\u7D046\u6841\u306B\u76F8\u5F53\u3059\u308B\u30021 + 24/60 + 51/60 + 10/60 = 1.41421296... \u3002(Image by Bill Casselman) \u6570\u5024\u89E3\u6790\uFF08\u3059\u3046\u3061\u304B\u3044\u305B\u304D\u3001Numerical Analysis\uFF09\u306F\u3001\u6570\u5B66\u306E\u4E00\u5206\u91CE\u3067\u3001\u89E3\u6790\u7684\u306B\u89E3\u304F\u3053\u3068\u304C\u4E0D\u53EF\u80FD\u306A\u6570\u5B66\u4E0A\u306E\u554F\u984C\u3092\u6570\u5024\u7684\u306B\u89E3\u304F\u624B\u6CD5\u306B\u95A2\u3059\u308B\u5B66\u554F\u3002 \u53F2\u4E0A\u6700\u521D\u306E\u6570\u5B66\u7684\u8A18\u8FF0\u306E1\u3064\u3068\u3057\u3066\u3001\u30D0\u30D3\u30ED\u30CB\u30A2\u306E\u7C98\u571F\u677F YBC 7289 \u304C\u3042\u308B\u3002\u3053\u308C\u306F\u3001\u516D\u5341\u9032\u6CD5\u3067 &lt;math&gt;\\sqrt{2}&lt;/math&gt; \uFF08\u5358\u4F4D\u77E9\u5F62\u306E\u5BFE\u89D2\u7DDA\u306E\u9577\u3055\uFF09\u306E\u6570\u5024\u7684\u8FD1\u4F3C\u3092\u793A\u3057\u305F\u3082\u306E\u3067\u3042\u308B\u3002\u4E09\u89D2\u5F62\u306E\u8FBA\u306E\u9577\u3055\u3092\u8A08\u7B97\u3067\u304D\u308B\u3053\u3068\uFF08\u305D\u3057\u3066\u3001\u5E73\u65B9\u6839\u3092\u8A08\u7B97\u3067\u304D\u308B\u3053\u3068\uFF09\u306F\u3001\u7279\u306B\u5EFA\u7BC9\u306B\u304A\u3044\u3066\u306F\u91CD\u8981\u3067\u3042\u308B\u3002\u4F8B\u3048\u3070\u3001\u7E26\u6A2A\u305D\u308C\u305E\u308C2\u30E1\u30FC\u30C8\u30EB\u306E\u6B63\u65B9\u5F62\u306E\u58C1\u306E\u5BFE\u89D2\u7DDA\u306F &lt;math&gt;\\sqrt{8} \\approx 2.83&lt;/math&gt; \u30E1\u30FC\u30C8\u30EB\u3068\u306A\u308B\u3002 \u6570\u5024\u89E3\u6790\u306F\u3001\u3053\u306E\u3088\u3046\u306A\u5B9F\u7528\u7684\u8A08\u7B97\u306E\u9577\u3044\u4F1D\u7D71\u306B\u7D9A\u304F\u3082\u306E\u3067\u3042\u308B\u3002\u30D0\u30D3\u30ED\u30CB\u30A2\u306E &lt;math&gt;\\sqrt{2}&lt;/math&gt; \u306E\u8FD1\u4F3C\u306E\u3088\u3046\u306B\u3001\u73FE\u4EE3\u306E\u6570\u5024\u89E3\u6790\u3082\u6B63\u78BA\u306A\u89E3\u3092\u6C42\u3081\u3088\u3046\u3068\u3059\u308B\u3082\u306E\u3067\u306F\u306A\u3044\u3002\u4F55\u6545\u306A\u3089\u3001\u6B63\u78BA\u306A\u89E3\u3092\u6709\u9650\u6642\u9593\u3067\u6C42\u3081\u308B\u3053\u3068\u306F\u4E0D\u53EF\u80FD\u3060\u304B\u3089\u3067\u3042\u308B\u3002\u305D\u306E\u4EE3\u308F\u308A\u3001\u6570\u5024\u89E3\u6790\u306E\u591A\u304F\u306F\u3042\u308B\u7A0B\u5EA6\u306E\u8AA4\u5DEE\u306E\u7BC4\u56F2\u5185\u306E\u8FD1\u4F3C\u89E3\u3092\u6C42\u3081\u3088\u3046\u3068\u3059\u308B\u3002 \u6570\u5024\u89E3\u6790\u306F\u5DE5\u5B66\u304A\u3088\u3073\u81EA\u7136\u79D1\u5B66\u306E\u3042\u3089\u3086\u308B\u5206\u91CE\u3067\u5FDC\u7528\u3055\u308C\u300121\u4E16\u7D00\u306B\u5165\u3063\u3066\u304B\u3089\u306F\u751F\u547D\u79D1\u5B66\u3084\u82B8\u8853\u3067\u3082\u79D1\u5B66\u6280\u8853\u8A08\u7B97\u304C\u5FDC\u7528\u3055\u308C\u308B\u3088\u3046\u306B\u306A\u3063\u3066\u304D\u305F\u3002\u5E38\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306F\u5929\u4F53\uFF08\u60D1\u661F\u3001\u6052\u661F\u3001\u5C0F\u5B87\u5B99\uFF09\u306E\u8ECC\u9053\u306E\u8A08\u7B97\u306B\u73FE\u308C\u308B\u3002\u8CC7\u7523\u7BA1\u7406\u306B\u306F\u6700\u9069\u5316\u304C\u9069\u7528\u53EF\u80FD\u3067\u3042\u308B\u3002\u6570\u5024\u7DDA\u578B\u4EE3\u6570\u306F\u91CF\u5B50\u7269\u7406\u5B66\u306E\u57FA\u672C\u3067\u3042\u308B\u3002\u78BA\u7387\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3068\u30DE\u30EB\u30B3\u30D5\u9023\u9396\u306F\u533B\u5B66\u3084\u751F\u7269\u5B66\u306B\u304A\u3051\u308B\u751F\u4F53\u7D30\u80DE\u306E\u30B7\u30DF\u30E5\u30EC\u30FC\u30B7\u30E7\u30F3\u306E\u57FA\u672C\u3067\u3042\u308B\u3002 \u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u304C\u767A\u660E\u3055\u308C\u308B\u4EE5\u524D\u3001\u6570\u5024\u624B\u6CD5\u306F\u5DE8\u5927\u306A\u6570\u8868\u3092\u4EBA\u9593\u304C\u5185\u633F\u3059\u308B\u306E\u304C\u4E3B\u3060\u3063\u305F\u3002\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u767A\u9054\u4EE5\u5F8C\u306F\u6570\u5024\u89E3\u6790\u306E\u8A08\u7B97\u304C\u5BB9\u6613\u3068\u306A\u3063\u305F\u305F\u3081\u6570\u8868\u304C\u4F7F\u308F\u308C\u308B\u3053\u3068\u306F\u307B\u3068\u3093\u3069\u306A\u304F\u306A\u308A\u3001\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u3067\u5FC5\u8981\u306A\u95A2\u6570\u3092\u5FC5\u8981\u306A\u7CBE\u5EA6\u3067\u8A08\u7B97\u3067\u304D\u308B\u3088\u3046\u306B\u306A\u3063\u305F\u3002\u3057\u304B\u3057\u305D\u306E\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u3067\u3055\u3048\uFF0C\u73FE\u5728\u306E\u591A\u304F\u306E\u30D7\u30ED\u30BB\u30C3\u30B5\u3067\u306F\u30BD\u30D5\u30C8\u30A6\u30A7\u30A2\u7684\u306A\u6570\u8868\u306E\u5185\u633F\u306B\u3088\u308B\u9AD8\u901F\u5316\u3092\u884C\u3046\u3053\u3068\u304C\u73FE\u5B9F\u7684\u3068\u306A\u3063\u3066\u3044\u308B\u3002\u5185\u633F\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u306F\u3001\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306A\u3069\u3092\u89E3\u304F\u969B\u306B\u30BD\u30D5\u30C8\u30A6\u30A7\u30A2\u304C\u5229\u7528\u3059\u308B\u3002"@ja ,
		"Analiza numeric\u0103 este studiul algoritmilor pentru problemele \u00EEn matematica continu\u0103. Aceasta \u00EEnseamn\u0103 ca ea este preocupat\u0103 \u00EEn principal cu variabile reale sau complexe, analiza linear\u0103 numeric\u0103 peste c\u00EEmpul numerelor reale sau complexe, solu\u0163iile ecua\u0163iilor diferen\u0163iale, sau a problemelor \u00EEnrudite din \u015Ftiin\u0163e fizice \u015Fi inginerie."@ro ,
		"Numeerinen analyysi on matematiikan osa-alue, joka pyrkii l\u00F6yt\u00E4m\u00E4\u00E4n likim\u00E4\u00E4r\u00E4isratkaisuja matemaattisiin ongelmiin, joita ei voi ratkaista tarkasti. Numeerisia menetelmi\u00E4 sovelletaan usein muun muassa fysiikan tarpeisiin esimerkiksi differentiaaliyht\u00E4l\u00F6iden ratkaisemiseksi. Numeerisia menetelmi\u00E4 ovat esimerkiksi yht\u00E4l\u00F6iden numeerinen ratkaiseminen, approksimointi ja numeerinen integrointi. Esimerkki numeerisen analyysin menetelmist\u00E4 on haarukointimenetelm\u00E4, jolla etsit\u00E4\u00E4n jatkuvan funktion nollakohtia. Haarukointimenetelm\u00E4n algoritmi on seuraava: Valitaan lukuv\u00E4li, jolla tutkittava funktio on m\u00E4\u00E4ritelty ja jonka p\u00E4\u00E4tepisteiss\u00E4 funktio saa erimerkkiset arvot. Lyhennet\u00E4\u00E4n v\u00E4li\u00E4 jommasta kummasta p\u00E4\u00E4st\u00E4 siten, ett\u00E4 funktio saa erimerkkiset arvot v\u00E4lin p\u00E4\u00E4tepisteiss\u00E4. Toistetaan kunnes haluttu tarkkuus on saavutettu."@fi ,
		"Ficheiro:Ybc7289-bw. jpg Clay tablet Babil\u00F4nio YBC 7289(c. 1800\u20131600 BCE) com anota\u00E7\u00F5es. (Imagem por Bill Casselman) A an\u00E1lise num\u00E9rica \u00E9 um ramo da matem\u00E1tica que estuda m\u00E9todos construtivos (na forma de algoritmos) que convergem para entidades matem\u00E1ticas cuja exist\u00EAncia foi demonstrada. Um m\u00E9todo num\u00E9rico apresenta uma sucess\u00E3o que converge para o valor exato. Cada termo dessa sucess\u00E3o deve ser visto como uma aproxima\u00E7\u00E3o - que \u00E9 poss\u00EDvel calcular com um n\u00FAmero finito de opera\u00E7\u00F5es elementares. \u00C9 objetivo da an\u00E1lise num\u00E9rica encontrar sucess\u00F5es que aproximem os valores exatos com um n\u00FAmero m\u00EDnimo de opera\u00E7\u00F5es elementares. Um dos escritos matem\u00E1ticos mais antigos \u00E9 o tablet babil\u00F4nio YBC 7289, que fornece uma aproxima\u00E7\u00E3o sexagesimal de &lt;math&gt;\\sqrt{2}&lt;/math&gt;, o comprimento da diagonal de um quadrado unit\u00E1rio. Ser capaz de calcular as faces de um tri\u00E2ngulo (e assim, sendo capaz de calcular ra\u00EDzes quadradas) \u00E9 extremamente importante, por exemplo, em carpintaria e constru\u00E7\u00E3o. Em uma parede quadrada que tem dois metros por dois metros, uma diagonal deve medir &lt;math&gt;\\sqrt{8} \\approx 2.83&lt;/math&gt; metros."@pt ,
		"El an\u00E1lisis o c\u00E1lculo num\u00E9rico es la rama de las matem\u00E1ticas que se encarga de dise\u00F1ar algoritmos para, a trav\u00E9s de n\u00FAmeros y reglas matem\u00E1ticas simples simular procesos matem\u00E1ticos m\u00E1s complejos aplicados a procesos del mundo real."@es ,
		"Analiza numeryczna to zbiorcza nazwa wszystkich dzia\u0142\u00F3w matematyki, kt\u00F3re zajmuj\u0105 si\u0119 badaniem struktur ci\u0105g\u0142ych, to znaczy zawieraj\u0105cych zbiory nieprzeliczalne, kt\u00F3rej g\u0142\u00F3wnym zadaniem jest badanie mo\u017Cliwo\u015Bci realizacji oblicze\u0144 przybli\u017Conych, oraz analiza powsta\u0142ych na skutek zaokr\u0105glenia b\u0142\u0119d\u00F3w. Pocz\u0105tek bada\u0144 nad analiz\u0105 numeryczn\u0105 to niekt\u00F3re badania prowadzone nad natur\u0105 ca\u0142ek, rozwi\u0105zywania r\u00F3wna\u0144 r\u00F3\u017Cniczkowych, teori\u0105 oblicze\u0144 czy metod numerycznych. Prawdziwy rozw\u00F3j analizy numerycznej jako osobnej dziedziny matematyki nast\u0105pi\u0142 z wynalezieniem komputer\u00F3w, gdy wa\u017Cne sta\u0142y si\u0119 odpowiedzi na pytania czym jest obliczanie, jak liczy\u0107 na komputerze bezpiecznie, czy jak tworzy\u0107 modele matematyczne, zbiory liczb i zale\u017Cno\u015Bci tworz\u0105ce np. program komputerowy przewiduj\u0105cy pogod\u0119 na podstawie danych pogodowych. Analiza numeryczna jako ga\u0142\u0105\u017A matematyki zawiera w sobie nast\u0119puj\u0105ce poddzia\u0142y: Teoria oblicze\u0144 Optymalizacja Teoria zagadnie\u0144 w\u0142asnych Numeryczna algebra liniowa Analiza b\u0142\u0119d\u00F3w Metody numeryczne Przy czym ostatnie metody numeryczne s\u0105 poniek\u0105d \"zwie\u0144czeniem\" dzie\u0142a, zbiorem praktycznych algorytm\u00F3w bazuj\u0105cych silnie na podstawach teoretycznych zawieraj\u0105cych si\u0119 w pozosta\u0142ych dzia\u0142ach analizy numerycznej."@pl ,
		"L'analisi numerica (detta anche calcolo numerico o calcolo scientifico) \u00E8 una disciplina che rientra nella classe della matematica applicata. Il suo obiettivo \u00E8 di sviluppare metodi per la risoluzione \"pratica\" di problemi matematici nel continuo tramite algoritmi che siano stabili, nel senso che non amplifichino gli errori inevitabilmente presenti sui dati di partenza siano efficienti, ossia abbiano basso costo computazionale, nel senso che la soluzione possa essere fornita da un calcolatore in un tempo accettabile. Si noti che la soluzione calcolata dall'algoritmo (detta anche soluzione numerica) \u00E8 sempre un'approssimazione di quella esatta: un algoritmo non ha ovviamente interesse se la soluzione calcolata si discosta molto da quella esatta. La maggior parte delle soluzioni a problemi di analisi numerica sono fondate sull'algebra lineare. Non vanno peraltro trascurati i contributi della combinatorica e della geometria, come pure i collegamenti con i metodi probabilistici e fisico matematici. Alcuni problemi della matematica del continuo possono essere risolti con algoritmi che risolvono il problema in un numero finito (e possibilmente noto a priori) di passi. Questi metodi sono detti metodi diretti. Tuttavia, per la maggior parte dei problemi numerici non ci sono metodi diretti. In tali casi, \u00E8 spesso possibile usare un metodo iterativo. Un tale metodo inizia da un tentativo, e trova approssimazioni successive che sperabilmente convergono alla soluzione. Sono metodi iterativi l'algoritmo di Gauss-Jordan per risolvere i sistemi di equazioni lineari, e l'algoritmo del simplesso in programmazione lineare. Anche quando esiste un metodo diretto, a volte \u00E8 preferibile un metodo iterativo perch\u00E9 pi\u00F9 efficiente o pi\u00F9 stabile, soprattutto quando si devono trattare matrici di dimensioni considerevoli (ad esempio una 1000x1000)."@it ;
	rdfs:comment	"File:Ybc7289-bw. jpg Babylonian clay tablet YBC 7289(c. 1800\u20131600 BCE) with annotations."@zh ,
		"Analiza numeric\u0103 este studiul algoritmilor pentru problemele \u00EEn matematica continu\u0103. Aceasta \u00EEnseamn\u0103 ca ea este preocupat\u0103 \u00EEn principal cu variabile reale sau complexe, analiza linear\u0103 numeric\u0103 peste c\u00EEmpul numerelor reale sau complexe, solu\u0163iile ecua\u0163iilor diferen\u0163iale, sau a problemelor \u00EEnrudite din \u015Ftiin\u0163e fizice \u015Fi inginerie."@ro ,
		"L'analisi numerica (detta anche calcolo numerico o calcolo scientifico) \u00E8 una disciplina che rientra nella classe della matematica applicata."@it ,
		"Numeerinen analyysi on matematiikan osa-alue, joka pyrkii l\u00F6yt\u00E4m\u00E4\u00E4n likim\u00E4\u00E4r\u00E4isratkaisuja matemaattisiin ongelmiin, joita ei voi ratkaista tarkasti. Numeerisia menetelmi\u00E4 sovelletaan usein muun muassa fysiikan tarpeisiin esimerkiksi differentiaaliyht\u00E4l\u00F6iden ratkaisemiseksi. Numeerisia menetelmi\u00E4 ovat esimerkiksi yht\u00E4l\u00F6iden numeerinen ratkaiseminen, approksimointi ja numeerinen integrointi."@fi ,
		"\u041E\u0431\u0447\u0438\u0301\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0301\u0442\u0438\u043A\u0430 \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438, \u0449\u043E \u0432\u043A\u043B\u044E\u0447\u0430\u0454 \u043A\u043E\u043B\u043E \u043F\u0438\u0442\u0430\u043D\u044C, \u0437\u0432'\u044F\u0437\u0430\u043D\u0438\u0445 \u0437 \u0432\u0438\u043A\u043E\u043D\u0430\u043D\u043D\u044F\u043C \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u044C \u0456 \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u0430\u043D\u043D\u044F\u043C \u043A\u043E\u043C\u043F'\u044E\u0442\u0435\u0440\u0456\u0432. \u0423 \u0431\u0456\u043B\u044C\u0448 \u0432\u0443\u0437\u044C\u043A\u043E\u043C\u0443 \u0440\u043E\u0437\u0443\u043C\u0456\u043D\u043D\u0456, \u043E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u2014 \u0442\u0435\u043E\u0440\u0456\u044F \u0447\u0438\u0441\u0435\u043B\u044C\u043D\u0438\u0445 \u043C\u0435\u0442\u043E\u0434\u0456\u0432 \u0440\u043E\u0437\u0432\u2019\u044F\u0437\u0443\u0432\u0430\u043D\u043D\u044F \u0442\u0438\u043F\u043E\u0432\u0438\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u0437\u0430\u0434\u0430\u0447."@uk ,
		"Die numerische Mathematik, kurz Numerik genannt, besch\u00E4ftigt sich als Teilgebiet der Mathematik mit der Konstruktion und Analyse von Algorithmen f\u00FCr kontinuierliche mathematische Probleme. Hauptanwendung ist dabei die Berechnung von L\u00F6sungen mit Hilfe von Computern."@de ,
		"Say\u0131sal y\u00F6ntemler, elde bulunan nicel (say\u0131sal) ve/veya nitel(niteliksel) de\u011Ferler \u0131\u015F\u0131\u011F\u0131nda \u00FCretim, ula\u015F\u0131m, konu\u015Fland\u0131rma gibi faaliyetlerde en ak\u0131lc\u0131 ve verimli karar\u0131 verme bilim dal\u0131d\u0131r. \u00C7\u00F6z\u00FCm problemin \u00F6zelli\u011Fine ba\u011Fl\u0131 olsa da genel anlamda minimum (en az) ya da maksimumdan (en \u00E7ok) ziyade optimumdur (en iyi). Say\u0131sal y\u00F6ntemler en iyiye ula\u015Fma \u00E7abas\u0131nda bir\u00E7ok matematiksel, istatistiksel ve s\u0131n\u0131fland\u0131rma yollu y\u00F6ntem i\u00E7erir."@tr ,
		"Ficheiro:Ybc7289-bw. jpg Clay tablet Babil\u00F4nio YBC 7289(c. 1800\u20131600 BCE) com anota\u00E7\u00F5es. (Imagem por Bill Casselman) A an\u00E1lise num\u00E9rica \u00E9 um ramo da matem\u00E1tica que estuda m\u00E9todos construtivos (na forma de algoritmos) que convergem para entidades matem\u00E1ticas cuja exist\u00EAncia foi demonstrada. Um m\u00E9todo num\u00E9rico apresenta uma sucess\u00E3o que converge para o valor exato."@pt ,
		"Numerieke wiskunde is een deelgebied van de wiskunde waarin algoritmes voor problemen in de continue wiskunde bestudeerd worden (in tegenstelling tot discrete wiskunde). Dit betekent dat het vooral gaat over re\u00EBle of complexe variabelen, de oplossing van differentiaalvergelijkingen en andere vergelijkbare problemen die optreden in de natuurkunde en techniek."@nl ,
		"File:Ybc7289-bw. jpg Babylonian clay tablet YBC 7289(c. 1800\u20131600 BCE) with annotations. (Image by Bill Casselman) Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). One of the earliest mathematical writings is the Babylonian tablet YBC 7289, which gives a sexagesimal numerical approximation of &lt;math&gt;\\sqrt{2}&lt;/math&gt;, the length of the diagonal in a unit square."@en ,
		"F\u00E1jl:Ybc7289-bw. jpg YBC 7289-es babiloni agyagt\u00E1bla(ie. 1800\u20131600) A numerikus anal\u00EDzis olyan algoritmusokkal foglalkozik, melyek folytonos (teh\u00E1t nem diszkr\u00E9t) matematikai feladatokat oldanak meg. Az egyik legr\u00E9gebbi matematikai \u00EDr\u00E1s az YBC 7289-es sz\u00E1m\u00FA Babil\u00F3niai agyagt\u00E1bla, amely 60-as sz\u00E1mrendszerben jegyezte le a &lt;math&gt;\\sqrt{2}&lt;/math&gt; numerikus k\u00F6zel\u00EDt\u00E9s\u00E9t, ami egy egys\u00E9g n\u00E9gyzet \u00E1tl\u00F3j\u00E1nak hossza."@hu ,
		"Analiza numeryczna to zbiorcza nazwa wszystkich dzia\u0142\u00F3w matematyki, kt\u00F3re zajmuj\u0105 si\u0119 badaniem struktur ci\u0105g\u0142ych, to znaczy zawieraj\u0105cych zbiory nieprzeliczalne, kt\u00F3rej g\u0142\u00F3wnym zadaniem jest badanie mo\u017Cliwo\u015Bci realizacji oblicze\u0144 przybli\u017Conych, oraz analiza powsta\u0142ych na skutek zaokr\u0105glenia b\u0142\u0119d\u00F3w. Pocz\u0105tek bada\u0144 nad analiz\u0105 numeryczn\u0105 to niekt\u00F3re badania prowadzone nad natur\u0105 ca\u0142ek, rozwi\u0105zywania r\u00F3wna\u0144 r\u00F3\u017Cniczkowych, teori\u0105 oblicze\u0144 czy metod numerycznych."@pl ,
		"L\u2019analyse num\u00E9rique est une discipline des math\u00E9matiques. Elle s\u2019int\u00E9resse tant aux fondements th\u00E9oriques qu\u2019\u00E0 la mise en pratique des m\u00E9thodes permettant de r\u00E9soudre, par des calculs purement num\u00E9riques, des probl\u00E8mes d\u2019analyse math\u00E9matique. Plus formellement, l\u2019analyse num\u00E9rique est l\u2019\u00E9tude des algorithmes permettant de r\u00E9soudre les probl\u00E8mes de math\u00E9matiques continues."@fr ,
		"El an\u00E1lisis o c\u00E1lculo num\u00E9rico es la rama de las matem\u00E1ticas que se encarga de dise\u00F1ar algoritmos para, a trav\u00E9s de n\u00FAmeros y reglas matem\u00E1ticas simples simular procesos matem\u00E1ticos m\u00E1s complejos aplicados a procesos del mundo real."@es ,
		"\u30D5\u30A1\u30A4\u30EB:Ybc7289-bw. jpg \u30D0\u30D3\u30ED\u30CB\u30A2\u306E\u7C98\u571F\u677F YBC 7289 \uFF08\u7D00\u5143\u524D1800-1600\u5E74\u9803\uFF09 2\u306E\u5E73\u65B9\u6839\u306E\u8FD1\u4F3C\u5024\u306F60\u9032\u6CD5\u30674\u6841\u300110\u9032\u6CD5\u3067\u306F\u7D046\u6841\u306B\u76F8\u5F53\u3059\u308B\u30021 + 24/60 + 51/60 + 10/60 = 1.41421296..."@ja .
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