ЧМ / Введение в методы численного анализа
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Kbkl_fm fh`gh aZibkZlv \ \b^_
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j_rb\ wlh mjZ\g_gb_ hlghkbl_evgh ; N ihemqbf
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DZd b ^ey kemqZy k h^ghc i_j_f_gghc f_lh^ GvxlhgZ fh`gh fh^bnbpbjh\Zlv lZd qlh[u \uqbkeylv Ydh[bZg lhevdh \ h^ghc lhqd_
; N ; N : ; ) ; N
Kdhjhklv koh^bfhklb fh^bnbpbjh\Zggh]h f_lh^Z GvxlhgZ agZqbl_evgh gb`_ q_f |
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dhgklZglZ b ihkljhbf bl_jZpbhgguc ijhp_kk ih ko_f_ ; N |
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IZjZf_lj W ^he`_g [ulv lZdbf qlh[u \ hdj_klghklb j_r_gby \uihegyehkv ^hklZlhqgh_ |
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mkeh\b_ koh^bfhklb __? W :__ ]^_ ( _^bgbqgZy fZljbpZ |
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GZ ijZdlbd_ \uiheg_gb_ wlh]h mkeh\by ^hklZlhqgh keh`gh ijh\_jblv ihwlhfm agZq_gb_ |
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iZjZf_ljZ W \u[bjZxl ijh[guf iml_f ijh\_jyy \uiheg_gb_ g_h[oh^bfh]h mkeh\by |
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koh^bfhklb ihke_ \uiheg_gby dZ`^hc bl_jZpbb |
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?keb hdZ`_lky qlh gZ dZdhc eb[h bl_jZpbb wlh mkeh\b_ g_ \uihegy_lky lh g_h[oh^bfh baf_gblv agZq_gb_ iZjZf_ljZ W
L _ f Z IJB;EB@?GB? NMGDPBC BGL?JIHEYPBHGGUFB IHEBGHF:FB
Imklv nmgdpby I [ aZ^ZgZ ^ey ^bkdj_lgh]h gZ[hjZ lhq_d [L fgh`_kl\hf k\hbo agZq_gbc ILI [L l _ lZ[ebp_c b imklv lj_[m_lky gZclb ijb[eb`_ggh_ agZq_gb_ I [ ijb [ z [L Ijb ^hklZlhqgh ih^jh[ghc lZ[ebp_ l _ dh]^Z _[L [_ fZeh b [| [L fh`gh iheh`blv I [ | I [L beb
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< h[s_f kemqZ_ [m^_f aZf_gylv nmgdpbx I [ ihebghfhf kl_i_gb Q 3Q [ D D [ D [ DQ[Q
kh\iZ^Zxsbf k nmgdpb_c I [ \ Q lZ[ebqguo lhqdZo [ gZau\Z_fuo maeZfb bgl_jiheypbb |
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Kbkl_fZ mjZ\g_gbc fh`_l [ulv j_r_gZ _keb |
kj_^b maeh\ [ g_l kh\iZ^Zxsbo |
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Bkihevamy j_r_gb_ wlhc kbkl_fu bgl_jiheypbhgguc |
ihebghf fh`gh aZibkZlv \ \b^_ |
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ihebghfZ EZ]jZg`Z |
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Ihebghf EZ]jZg`Z m^h[gh bkihevah\Zlv _keb lj_[m_lky gZoh^blv ijb[eb`_gby jZaebqguo nmgdpbc aZ^Zgguo \ h^gbo b l_o `_ lZ[ebqguo lhqdZo < lZdbo kemqZyo fh`gh ij_^\Zjbl_evgh \uqbkeblv dhwnnbpb_glu EZ]jZg`Z
Z ^ey \uqbke_gby agZq_gbc nmgdpbc bkihevah\Zlv nhjfmem
AZf_lbf qlh agZq_gby dhwnnbpb_glh\ EZ]jZg`Z bg\ZjbZglgu hlghkbl_evgh ebg_cghc |
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ih^klZgh\db l _ _keb |
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?keb maeu bgl_jiheypbb jZ\ghhlklhysb_ b mihjy^hq_gu ih \_ebqbg_ lZd qlh [ |
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K FRQVWl _ [ |
[ LK lh bgl_jiheypbhgguc ihebghf fh`gh aZibkZlv \ nhjf_ GvxlhgZ |
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I_j\Zy bgl_jiheypbhggZy nhjfmeZ GvxlhgZ bf__l \b^ |
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Z \ujZ`_gby \b^Z |
dhg_qgu_ jZaghklb |
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jZaghklv i_j\h]h ihjy^dZ |
jZaghklv \lhjh]h ihjy^dZ |
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jZaghklv N ]h ihjy^dZ |
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<lhjZy bgl_jiheypbhggZy nhjfmeZ GvxlhgZ aZibku\Z_lky \ \b^_ |
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]^_ Bgl_jiheypbhggu_ ihebghfu \ nhjf_ GvxlhgZ m^h[gh bkihevah\Zlv _keb lhqdZ bgl_jihebjh\Zgby gZoh^blky \[ebab gZqZeZ i_j\Zy nhjfmeZ GvxlhgZ beb dhgpZ lZ[ebpu
\lhjZy nhjfmeZ GvxlhgZ Wlb ihebghfu bgl_j_kgu l_f qlh dZ`^Zy qZklbqgZy kmffZ i_j\uo P keZ]Z_fuo _klv bgl_jiheypbhgguc ihebghf P kl_i_gb ihkljh_gguc ih P i_j\uf ^ey i_j\hc nhjfmeu beb ihke_^gbf ^ey \lhjhc nhjfmeu lZ[ebqguf lhqdZf
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ih \_ebqbg_ dhlhjh]h fh`gh dklZlb hij_^_eblv b p_e_khh[jZaghklv ^Zevg_cr_]h m\_ebq_gby kl_i_gb bgl_jiheypbb
?keb lhqdZ bgl_jihebjh\Zgby [ e_`bl \[ebab dZdh]h eb[h \gmlj_gg_]h maeZ lh h[hagZqZy wlhl ma_e [ Z maeu ke_\Z hl g_]h hljbpZl_evgufb bg^_dkZfb [ [ K [ [
K b l ^ fh`gh aZibkZlv bgl_jiheypbhgguc ihebghf \ \b^_ i_j\hc nhjfmeu =ZmkkZ ^ey [ ! [
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Ijb bgl_jihebjh\Zgbb \[ebab k_j_^bgu lZ[ebpu l _ ijb [ | [ bkihevam_lky bgl_jiheypbhggZy nhjfmeZ GvxlhgZ ;_kk_ey
?keb lhqdZ bgl_jihebjh\Zgby [ kh\iZ^Z_l k k_j_^bghc hlj_adZ |
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bgl_jihebjh\Zgb_ gZ k_j_^bgm lh nhjfmeZ GvxlhgZ ;_kk_ey agZqbl_evgh mijhsZ_lky |
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Hrb[dZ ijb[eb`_gby nmgdpbb bgl_jiheypbhgguf ihebghfhf wlh jZaghklv 5Q [ I [ 3Q [ Bkihevamy l_hj_fm Jheey fh`gh ihemqblv ke_^mxsb_ \ujZ`_gby ^ey ih]j_rghklb bgl_jiheypbb
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AZf_lbf lZd`_ qlh ^ey g_dhlhjuo nmgdpbc I [ hij_^_e_gguo |
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bgl_jiheypbhgguc fgh]hqe_g 3 [ ihkljh_gguc ih agZq_gbyf I [ \ jZ\ghhlklhysbo maeZo [ |
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k jhklhf qbkeZ maeh\ Q \h\k_ g_ [m^_l bf_lv |
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m[u\Zxsmx ih]j_rghklv bgl_jihebjh\Zgby GZijbf_j ^ey nmgdpbb |
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mqZkld_ > @ ih]j_rghklv bgl_jiheypbb ijb jZ\ghhlklhysbo maeZo g_ klj_fblky d gmex |
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ijb m\_ebq_gbb Q Wlh h[mkeh\e_gh l_f qlh jZ\ghhlklhysb_ maeu g_ y\eyxlky emqrbfb k |
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lhqdb aj_gby mf_gvr_gby ih]j_rghklb bgl_jihebjh\Zgby ?keb bf__lky \hafh`ghklb |
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\u[hjZ maeh\ bgl_jihebjh\Zgby lh bo ke_^m_l \u[bjZlv lZd qlh[u h[_ki_qblv fbgbfmf |
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ih]j_rghklb bgl_jiheypbbPLQ_5 |
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[ _ LZdhfm lj_[h\Zgbx gZ hlj_ad_> @m^h\e_l\hjyxl |
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maeu ihebghfh\ Q_[ur_\Z |
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\uqbkey_fu_ ih nhjfme_ |
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kemqZ_ ijhba\hevgh]h hlj_adZ >D E@ maeu |
bgl_jiheypbb \uqbkeyxl ih |
nhjfme_ |
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Bgl_jiheypbhgguc ihebghf ihkljh_gguc ih lZdbf maeZf y\ey_lky Ze]_[jZbq_kdbf |
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ihebghfhf gZbemqr_]h ijb[eb`_gby |
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Dmkhqgh fgh]hqe_ggZy bgl_jiheypby Ihkdhevdm m\_ebq_gb_ kl_i_gb bgl_jiheyglZ g_ |
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\k_]^Z \_^_l d mf_gvr_gbx ih]j_rghklb bgl_jihebjh\Zgby ^ey \hkklZgh\e_gby agZq_gbc |
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nmgdpbb |
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ijhba\hevguo lhqdZo fh`gh ihevah\Zlvky nmgdpb_c dhlhjZy f_`^m ^\mfy |
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khk_^gbfb maeZfb y\ey_lky ihebghfhf aZ^Zgghc g_\ukhdhc kl_i_gb gZijbf_j i_j\hc |
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bgl_jiheypby gZau\Z_lky dmkhqgh ebg_cghc |
dmkhqgh |
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d\Z^jZlbqghc b l ^ |
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< kemqZ_ dmkhqgh ebg_cghc bgl_jiheypbb gZ dZ`^hf hlj_ad_ |
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ijb[eb`_gby nmgdpbb bkihevam_lky ihebghf |
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Z bgl_jiheygl ij_^klZ\ey_l |
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kh[hc ehfZgmx ebgbx khklhysmx ba hlj_adh\ ijyfuo Ijb dmkhqgh d\Z^jZlbqghc |
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bgl_jiheypbb bgl_jiheygl khklhbl ba hlj_adh\ iZjZ[he ijhoh^ysbo q_j_a ljb khk_^gbo |
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maeZ |
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ih^oh^ d bgl_jihebjh\Zgbx ijb\h^bl d lhfm qlh |
bgl_jiheygl |
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bgl_jiheypbb fh`_l g_ bf_lv ijhba\h^ghc ^Z`_ i_j\h]h ihjy^dZ |
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Dmkhqgh fgh]hqe_ggZy ]eZ^dZy bgl_jiheypby |
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dmkhqgh fgh]hqe_ggZy |
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bgl_jiheypbhggZy nmgdpby h[eZ^ZxsZy aZ^Zgguf qbkehf ijhba\h^guo \kx^m \dexqZy |
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maeu bgl_jihebjh\Zgby |
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Imklv nmgdpby I [ hij_^_e_gZ gZ hlj_ad_>D E@b ba\_klgu __ agZq_gby \ kbkl_f_ maeh\ |
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6 [ m^h\e_l\hjyxsZy ke_^mxsbf mkeh\byf |
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