Steffensenova metoda a její zobecnění
Predlozzena prace popisuje Steensenovu metodu jako variantu Newtonovy metody. Uvodni kapitola nastinuje problematiku reseni soustav nelinearnich rovnic. Druha kapitola predstavuje obe metody v oboru realnych cisel. Steensenova metoda je navíc odvozena z Aitkenovy metody pro urychleni konvergence jin...
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| Typ dokumentu: | VŠ práce nebo rukopis |
| Jazyk: | Čeština |
| Vydáno: |
2010
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| Témata: | |
| On-line přístup: | http://is.muni.cz/th/150986/prif_m/ |
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| 072 | 7 | |a 519.1/.8 |x Kombinatorika. Teorie grafů. Matematická statistika. Operační výzkum. Matematické modelování |2 Konspekt |9 13 | |
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| 100 | 1 | |a Švendová, Vendula, |d 1985- |7 mub2011667360 |% UČO 150986 |4 dis | |
| 242 | 1 | 0 | |a Steffensen's method and its generalization |y eng |
| 245 | 1 | 0 | |a Steffensenova metoda a její zobecnění |h [rukopis] / |c Vendula Švendová |
| 260 | |c 2010 | ||
| 300 | |a 44 l. | ||
| 500 | |a Vedoucí práce: Ivanka Horová | ||
| 502 | |a Diplomová práce (Mgr.)--Masarykova univerzita, Přírodovědecká fakulta, 2010 | ||
| 520 | 2 | |a Predlozzena prace popisuje Steensenovu metodu jako variantu Newtonovy metody. Uvodni kapitola nastinuje problematiku reseni soustav nelinearnich rovnic. Druha kapitola predstavuje obe metody v oboru realnych cisel. Steensenova metoda je navíc odvozena z Aitkenovy metody pro urychleni konvergence jinych iteracnich metod. Treti kapitola se zabyva teorii majorizace v Banachove prostoru. Ve ctvrte kapitole je pomoci teto teorie dokazana konvergence tzv. metod "Newtonova typu". Pata kapitola zobecnuje Steensenovu metodu, jako konkretni pripad metody Newtonova typu. Metoda je implementovana v programu Matlab. |% cze | |
| 520 | 2 | 9 | |a Presented work describes the study of Steffensen's method as a variant of Newton's method. Introductory chapter foreshadows the problem of solving nonlinear equations. The second chapter introduces both methods in the field of real numbers. Additionally, Steffensen's method is derived from Aitken method for the acceleration of convergence of other iterative methods. The third chapter covers the majorization theory in Banach spaces. In the fourth chapter, the convergence of the so-called "Newton's type" method is proven using this theory. The fifth chapter generalizes Steffensen's method as a specific case of the Newton's type method. The method is implemented in Matlab. |9 eng |
| 650 | 0 | 7 | |a nelineární rovnice |2 CZ-BrMU |
| 650 | 0 | 7 | |a numerické metody |7 ph169354 |2 czenas |
| 650 | 0 | 9 | |a numerical methods |2 eczenas |
| 655 | 7 | |a diplomové práce |7 fd132022 |2 czenas | |
| 655 | 9 | |a master's theses |2 eczenas | |
| 658 | |a Matematika |b Matematické modelování a numerické metody |c PřF N-MA NUMER (NUMER) |2 CZ-BrMU | ||
| 700 | 1 | |a Horová, Ivana, |d 1943- |7 jn20000810195 |% UČO 1951 |4 ths | |
| 710 | 2 | |a Masarykova univerzita. |b Ústav matematiky a statistiky |7 kn20091211007 |4 dgg | |
| 856 | 4 | 1 | |u http://is.muni.cz/th/150986/prif_m/ |
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