Учёба / lab_mat-met

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«F:L?F:LBQG1 F?LH>B < ?E?DLJHL?OGBP1»

>hg_pvd – >hg>LM – 2001

F1G1KL?JKL<H HK<1LB 1 G:MDB MDJ:2GB

>HG?PVDBC >?J@:<GBC L?OG1QGBC MG1<?JKBL?L

F ? L H > B Q G 1 < D : A 1 < D B

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«F:L?F:LBQG1 F?LH>B < ?E?DLJHL?OGBP1»

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>hg_pvd – >hg>LM – 2001

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MdeZ^Zq• H 1 Lhehqdh ^hp H < I•kdh\ZlkvdZ Zkbkl = K Q_dZ\kvdbc Zki

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HI?J:PI2 A F:LJBPYFB

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L_hj_lbqgL\i^hfhkli

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KmfZ lZ jiagbpy ^\ho fZljbpv

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>h[mlhd fZljbpv i ii^g_k_ggy €o m klmiigv

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3

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k kii\fgh`gbdi\

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^•e_ggy fZljbpv:

B/A \•^ih\•^Z} B*A-1; A\B \•^ih\•^Z} A-1*B,

^_ A-1 – h[_jg_gZ fZljbpy

J•r_ggy kbkl_f e•g•cgbo j•\gygv lbim X=A\B j_Ze•ah\Zgh m ML aZ ^hihfh]hx ki_p•Zevgh]h fhg•lhjZ ydbc \bdhjbklh\m} j•ag• Ze]hjblfb j•r_ggy m aZe_`ghkl• \•^ kljmdlmjb fZljbp• : GZijbdeZ^ ydsh : – ijh•a\hevgZ d\Z^jZlgZ fZljbpy lh ljbdmlgbc jhadeZ^ \bjZoh\m}lvky f_lh^hf \bdexq_gv =ZmkZ a qZkldh\bf \b[hjhf ]heh\gh]h _e_f_glZ

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4

h^_j`bfh fZljbpx Α L jhafijhf n*m ydZ fZ} gZa\m ljZgkihgvh\Zgh€ m \i^ghr_gg•

-$ % ≤ $% ;

-$ − % ≥ % − $ .

>h gZc[ievr e_]dh h[qbkex\Zgbo ghjf gZe_`Zlv gZklmigi ljb ghjfb

- dhjigv d\Z^jZlgbc ia kmfb d\Z^jZli\ fh^mei\ mkio _e_f_gli\ fZljbpi. M ML ^ey h[qbke_ggy ghjf fZljbp• •kgm} nmgdp•y norm:

norm : \•^ih\•^Z} $ ; norm : inf) \•^ih\•^Z} $ ;

QRUP: QRUP$ \•^ih\•^Z} $ .

5

H[_jg_ggy fZljbpv

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LZdbf qbghf ^ey \bagZq_ggy mk•o _e_f_gl•\ h[_jg_gh€ fZljbp• g_h[o•^gh jha\¶yaZlb n kbkl_f j•\gygv

6

P_c i•^o•^ qZklh \bdhjbklh\mxlv ijb fZrbggbo jhajZomgdZo Jha\¶yam\Zlb kbkl_fb j•\gygv fh`gZ [m^v-ydbf a \•^hfbo f_lh^•\ gZijbdeZ^ f_lh^hf =ZmkZ

M ML ^ey h[_jg_ggy fZljbpv \bdhjbklh\mxlv nmgdp•x inv(A).

1.1.6 <bagZqgbd fZljbp•

>ey h[qbkex\Zggy \bagZqgbdZ fh`gZ i_j_l\hjblb ihqZldh\m fZljbpx \ ljbdmlh\m nhjfm aZ ^hihfh]hx ijyfh]h oh^m f_lh^Z =ZmkZ lZ jhajZom\Zlb ^h[mlhd €€ ^•Z]hgZevgbo _e_f_gl•\

Ydsh m ko_f• ijyfh]h oh^m \bdhjbklh\m}lvky i_j_klZgh\dZ jy^d•\ lh lj_[Z \jZom\Zlb sh h^gZ lZdZ i_j_klZgh\dZ af•gx} agZd \bagZqgbdZ gZ ijhlbe_`gbc

M ML ^ey h[qbke_ggy \bagZqgbdZ fZljbp• \bdhjbklh\mxlv nmgdp•x det(A).

Ke•^ • jZg] fZljbp•

Ke•^hf d\Z^jZlgh€ fZljbp• : gZab\Zxlv kmfm €€ ^•Z]hgZevgbo _e_f_gl•\

WU( $) = ∑Q DLL . (1.14)

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M ML px hi_jZp•x \bdhgm} nmgdp•y trace(A).

JZg] fZljbp• : \bagZqZ} d•evd•klv e•g•cgh g_aZe_`gbo j•\gygv m \bo•^g•c kbkl_f• M ML px hi_jZp•x \bdhgm} nmgdp•y rank(A, tol).

AZ\^Zggy

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>ey g_iZjgbo \Zj•Zgl•\ h[qbkeblb h[_jg_gm fZljbpx ^h D ^ey iZjgbo – \bagZqgbd fZljbp• D <•^kmlg• jy^hd Z[h klh\i_pv ^hih\gblb qbkeZfb

7

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