01NM
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\OT1/cmr/m/n/10 Posledn^^S^^P ma-tici po-rovn^^Same s ma-tic^^S^^P na prav^^Se
stran^^Te ([][]2[][]) a do-sta-neme $[] = [][][]$, $[] = [][][][]\OML/cmm/m/it/
10 ^^N \OT1/cmr/m/n/10 =
[]
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\OT1/cmr/m/n/10 p^^Trechodu
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\OT1/cmr/m/n/10 nez^^Savisl^^Sych vlastn^^S^^Pch vek-tor^^Wu p^^Tr^^S^^Pslu^^Ts
ej^^S^^Pc^^S^^Pch k vlastn^^S^^Pmu ^^Tc^^S^^Pslu $\OML/cmm/m/it/10 ^^U$ \OT1/cm
r/m/n/10 se naz^^Syv^^Sa ge-o-me-t-rick^^Sa n^^Sasobnost.
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[][]\OT1/cmr/bx/n/10 Tvrzen^^S^^P 1.16. []\OT1/cmr/m/n/10 P^^Tr^^S^^Pm^^Sy chod
Gaus-sovy eli-mina^^Tcn^^S^^P me-tody je pro-ve-di-teln^^Sy (tj.
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\OT1/cmr/m/n/10 1.2.2.\OT1/cmr/m/it/10 Sch^^Sema je-din^^Seho d^^Telen^^S^^P s
hlavn^^S^^Pmi prvky.[] \OT1/cmr/m/n/10 Podm^^S^^Pnkou ^^Tre^^Tsitelnosti sou-s
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[]\OT1/cmr/m/n/10 Ozna^^Tcme $[][] [] [][]$ sloupce ma-tice $\OML/cmm/m/it/10 A
[]$\OT1/cmr/m/n/10 . Proto^^Tze plat^^S^^P $\OML/cmm/m/it/10 AA[] \OT1/cmr/m/n/
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\OT1/cmr/m/n/10 ([][] [] [][]) =
[]
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\OT1/cmr/m/n/10 2.1.3.\OT1/cmr/m/it/10 Nestacion^^Sarn^^S^^P me-tody.[] \OT1/c
mr/m/n/10 Itera^^Tcn^^S^^P me-tody se d^^Tel^^S^^P na sta-cion^^Sarn^^S^^P, kde
je po-sloup-nost ma-tic $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 H[]\OMS/cmsy/m/n/1
0 g[]$
[]
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[]\OT1/cmr/m/n/10 Ozna^^Tcme $\OML/cmm/m/it/10 B \OT1/cmr/m/n/10 = \OML/cmm/m/i
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m/m/it/10 B \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 I\OT1/cmr/m/n/10 )[] =$
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\OT1/cmr/m/n/10 kon-stantn^^S^^P n^^Sasobek to-hoto v^^Syrazu, tj. $\OML/cmm/m/
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[]\OT1/cmr/m/it/10 Konvergence. []\OT1/cmr/m/n/10 Plat^^S^^P $\OML/cmm/m/it/10
I \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 HA \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 I
\OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 !\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 D \OM
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ML/cmm/m/it/10 L \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 D \OMS/cmsy/m/n/10 ^^@ \OML
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\OT1/cmr/m/n/10 n^^Sasleduj^^S^^Pc^^S^^P: Ne-cht[] je d^^Sana itera^^Tcn^^S^^P
me-toda
[]
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\OT1/cmr/m/n/10 Nutnou podm^^S^^Pnkou pro kon-ver-genci me-tody p^^Tri li-bo-vo
ln^^Se volb^^Te $[]$ je tedy
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\OML/cmm/m/it/10 ^^U[]A[] \OMS/cmsy/m/n/10 ^^Y [][]\OML/cmm/m/it/10 A[] \OMS/cm
sy/m/n/10 ^^@ \OML/cmm/m/it/10 ^^U[][][][]$\OT1/cmr/m/n/10 , tj. $\OML/cmm/m/it
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[]\OT1/cmr/m/n/10 Podle ([][]36[][]) plat^^S^^P $\OML/cmm/m/it/10 A[]L[] \OT1/c
mr/m/n/10 = \OML/cmm/m/it/10 A[]AL[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 A[]L[]R
[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 A[]AL[]R[] \OT1/cmr/m/n/10 =$
[]
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[]\OT1/cmr/m/n/10 Podle p^^Tredpokladu exis-tuje jed-no-zna^^Tcn^^Sy roz-klad $
\OML/cmm/m/it/10 X[]L[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 L[]R[]$\OT1/cmr/m/n/
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Pkov^^Sa
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\OT1/cmr/m/n/10 kde $\OML/cmm/m/it/10 L[]$ \OT1/cmr/m/n/10 je doln^^S^^P troj^^
Suheln^^S^^Pkov^^Sa ma-tice s nu-lami na di-a-gon^^Sale, $\OML/cmm/m/it/10 L[]
[] O$\OT1/cmr/m/n/10 , a $\OML/cmm/m/it/10 R[]$ \OT1/cmr/m/n/10 je horn^^S^^P t
roj^^Suheln^^S^^Pkov^^Sa
[]
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[]\OT1/cmr/m/n/10 Podle p^^Tredpokladu exis-tuje jed-no-zna^^Tcn^^Sy roz-klad $
\OML/cmm/m/it/10 X[]L[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 L[]R[]$\OT1/cmr/m/n/
10 , kde $\OML/cmm/m/it/10 L[]$ \OT1/cmr/m/n/10 je doln^^S^^P troj^^Suheln^^S^^
Pkov^^Sa
[]
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\OT1/cmr/m/n/10 kde $\OML/cmm/m/it/10 L[]$ \OT1/cmr/m/n/10 je doln^^S^^P troj^^
Suheln^^S^^Pkov^^Sa ma-tice s nu-lami na di-a-gon^^Sale, $\OML/cmm/m/it/10 L[]
[] O$\OT1/cmr/m/n/10 , a $\OML/cmm/m/it/10 R[]$ \OT1/cmr/m/n/10 je horn^^S^^P t
roj^^Suheln^^S^^Pkov^^Sa
[]
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\OT1/cmr/m/n/10 kde $\OML/cmm/m/it/10 L[]$ \OT1/cmr/m/n/10 je doln^^S^^P troj^^
Suheln^^S^^Pkov^^Sa ma-tice s nu-lami na di-a-gon^^Sale, $\OML/cmm/m/it/10 L[]
[] O$\OT1/cmr/m/n/10 , a $\OML/cmm/m/it/10 R[]$ \OT1/cmr/m/n/10 je horn^^S^^P t
roj^^Suheln^^S^^Pkov^^Sa
[]
[34]
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[]
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[]\OT1/cmr/m/n/10 Diagon^^Saln^^S^^P prvky ve sloupc^^S^^Pch $1[] [] []\OML/cmm
/m/it/10 r \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 1[]\OML/cmm/m/it/10 t \OT1/cmr/
m/n/10 + 1[] [] []\OML/cmm/m/it/10 n$ \OT1/cmr/m/n/10 kon-ver-guj^^S^^P k vlast
n^^S^^Pm ^^Tc^^S^^Psl^^Wum $\OML/cmm/m/it/10 ^^U[][] [] []^^U[][]^^U[][] [] []^
^U[]$
[]
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[]\OT1/cmr/m/n/10 Ve sloupc^^S^^Pch $\OML/cmm/m/it/10 r[] [] []t$ \OT1/cmr/m/n/
10 kon-ver-guj^^S^^P k nule obecn^^Te pouze prvky v ^^Tr^^Sadc^^S^^Pch
[]
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\OT1/cmr/m/n/10 exis-tuj^^S^^P-li vz^^Sajemn^^Te r^^Wuzn^^Sa ^^Tc^^S^^Psla $\OM
L/cmm/m/it/10 k[][] [] []k[] \OMS/cmsy/m/n/10 2 []$ \OT1/cmr/m/n/10 tak, ^^Tze
[]
) [35] (./kapitola5.tex
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\OT1/cmr/m/n/10 6.2.\OT1/cmr/bx/n/10 Newtonova me-toda.[][] \OT1/cmr/m/n/10 P^
^Trepi^^Tsme nyn^^S^^P sou-stavu ([][]47[][]) do vek-to-rov^^Se po-doby $[]([])
= []$, kde $[](\OML/cmm/m/it/10 x[]; [] ; x[]\OT1/cmr/m/n/10 ) =
[]
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\OT1/cmr/m/n/10 Podle p^^Tredpokladu 3 proto exis-tuje ta-kov^^Se okol^^S^^P $\
OML/cmm/m/it/10 R \OMS/cmsy/m/n/10 ^^Z \OML/cmm/m/it/10 G$ \OT1/cmr/m/n/10 ^^Tr
e^^Tsen^^S^^P $[]$, ^^Tze pro ka^^Tzd^^Se $[] \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/
10 R$ \OT1/cmr/m/n/10 plat^^S^^P $[] \OMS/cmsy/m/n/10 ^^T
[]
) [43] (./kapitola7.tex [44
] [45]
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[][][][]\OT1/cmr/m/n/8 D^^Sale pro stru^^Tcnost ne-bu-deme zd^^Wuraz^^Tnovat, ^
^Tze nu-lov^^Se ^^Tcleny ve jme-no-va-tel^^S^^Pch jsou vy-
[]
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\OT1/cmr/m/n/8 nech^^Sany, tak^^Tze nap^^Tr. m^^S^^Psto $(\OML/cmm/m/it/8 x[] \
OMS/cmsy/m/n/8 ^^@ \OML/cmm/m/it/8 x[]\OT1/cmr/m/n/8 ) [] (\OML/cmm/m/it/8 x[]
\OMS/cmsy/m/n/8 ^^@ \OML/cmm/m/it/8 x[]\OT1/cmr/m/n/8 )(\OML/cmm/m/it/8 x[] \OM
S/cmsy/m/n/8 ^^@ \OML/cmm/m/it/8 x[]\OT1/cmr/m/n/8 ) [] (\OML/cmm/m/it/8 x[] \O
MS/cmsy/m/n/8 ^^@ \OML/cmm/m/it/8 x[]\OT1/cmr/m/n/8 )$ bu-deme ps^^Sat jen
[]
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[]\OT1/cmr/m/it/10 Pozn^^Samka. []\OT1/cmr/m/n/10 V praxi vych^^Saz^^S^^Pme z d
i-fe-ren^^Tcn^^S^^Pho sch^^Sematu. Sta^^Tc^^S^^P z n^^Tej ov^^Tsem spo^^Tc^^S^^
Ptat jen $\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/1
0 )[]\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[][]x[]\OT1/cmr/m/n/1
0 )[] [] []\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[][] [] ; x[]\O
T1/cmr/m/n/10 )$.
[]
[47] [48]) [49] (./kapitola8.tex [50
] [51]) [52] (./kapitola9.tex
Underfull \hbox (badness 10000) in paragraph at lines 64--65
[][]\OT1/cmr/bx/n/10 Tvrzen^^S^^P 9.1. []\OT1/cmr/m/n/10 Newtonova-Cotesova ^^T
c^^S^^Psla $\OML/cmm/m/it/10 I[]$ \OT1/cmr/m/n/10 jsou sy-me-t-rick^^Sa v $\OML
/cmm/m/it/10 i$\OT1/cmr/m/n/10 , tj.
[]
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\OMS/cmsy/m/n/10 ^^@[]\OML/cmm/m/it/10 I[]$ $\OT1/cmr/m/n/10 (\OML/cmm/m/it/10
i \OMS/cmsy/m/n/10 2 f\OT1/cmr/m/n/10 0[] [] []\OML/cmm/m/it/10 m \OMS/cmsy/m/n
/10 ^^@ \OT1/cmr/m/n/10 2\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 )$. Od-tud je z^^Tre
jm^^Se, ^^Tze
[]
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\OT1/cmr/m/n/10 Jednotliv^^Se in-tegr^^Saly vypo^^Tcteme po-moc^^S^^P New-to-no
v^^Sych-Cotesov^^Sych for-mul^^S^^P pro
[]
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\OT1/cmr/m/n/10 Jednotliv^^Se in-tegr^^Saly vypo^^Tcteme po-moc^^S^^P New-to-no
v^^Sych-Cotesov^^Sych for-mul^^S^^P pro
[]
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\OT1/cmr/m/n/10 Jednotliv^^Se in-tegr^^Saly vypo^^Tcteme po-moc^^S^^P New-to-no
v^^Sych-Cotesov^^Sych for-mul^^S^^P pro
[]
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