Analysis numerica

Analysis numerica est pars mathematicae adhibitae ubi coluntur algorithmi ad problemata continua solvenda, hoc est, problemata in quibus quantitates sunt numeri reales aut complexi (quae sunt problemata analysis). Quamquam bonum est problemata exacte solvere, potest melius esse approximationem habere, si celerius computari potest.

Historia

Tabula argillacea Babylonica, c. 1800-1600 a.C.n. Magnitudo lateris quadratae est 30. Prope diagonalem sunt numeri (1, 24, 51, 10) et (42, 25, 35), hoc est 1 + 24/60 + 51/60² + 10/60³ = 1.414213... vel fere

{\sqrt {2}}

, et 42 + 25/60 + 35/60² = 42.426388..., qui est (paene) magnitudo diagonalis quadratae.^[1]

Periti Babylonici numeros irrationales calculabant cum diagonales quadratas mensurarent.^[2] Sciebant aequationes quadraticas resolvere et magnitudines laterum figurarum regularium calculare.^[3]

Aegypti quoque quantitates irrationales calculabant.^[4]

Quamquam Babyloni et Aegypti algorithmos habebant et sciebant calculare, mathematici Graeci regulas generales invenerunt, et demonstraverunt has regulas correctas esse.^[5]

Mathematici hodierni non solum theoremata sed etiam methodos numericas inveniunt. Isaacus Newtonus algorithmum proponit ad integrale approximandum. Carolus Fridericus Gauss plurimos algorithmos numericos creavit.^[6]

Computatris potest plura et celerius calculare.

Algorithmi magni momenti

Methodus Newtoni ad integrum approximandum
Eliminatio Gaussiania, ad matricem invertendam
Algorithmus "simplex" appellatus, qui invenit valorem optimum qui resolvit aequationes et inaequationes linearium
Transformatio Fourierana

Notae

↑ Yale Babylonian Collection BC 7289
↑ Neugebauer 1957:34 sqq.
↑ Neugebauer 1957:41, 47.
↑ Neugebauer, ch. 4.
↑ Cuomo 2000:4-5.
↑ Trefethen 2008:605.

Nexus interni

Theoria numerorum

Bibliographia

Cuomo, S. 2000. Ancient Mathematics. Londinii: Routledge.
Golub, Gene H., et Charles F. Van Loan. 1986. Matrix Computations. Ed. 3a. Johns Hopkins University Press. ISBN 080185413X.
Higham, Nicholas J. 1996. Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics. ISBN 0898713552.
Hildebrand, F. B. 1974. Introduction to Numerical Analysis. Ed. 2a. McGraw-Hill. ISBN 0070287619.
Leader, Jeffery J. 2004. Numerical Analysis and Scientific Computation. Addison Wesley. ISBN 0201734990.
Neugebauer, Otto. 1957, 1969. The Exact Sciences in Antiquity. Providence, 1957. Novi Eboraci, 1969.
Trefethen, Lloyd N. 2008. Numerical Analysis. In Princeton Companion to Mathematics, edd. Timothy Gowers, June Barrow-Green, et Imre Leader, 604-615. Princetoniae.

[1] Yale Babylonian Collection BC 7289

[2] Neugebauer 1957:34 sqq.

[3] Neugebauer 1957:41, 47.

[4] Neugebauer, ch. 4.

[5] Cuomo 2000:4-5.

[6] Trefethen 2008:605.

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