Учёба / lab_mat-met
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(14.2) |
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Ydsh \L^hfLihqZldh\LgZ[eb`_ggy dhj_gL\ |
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(14.3) |
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lh ^ey €o mlhqg_ggy \bdhjbklh\mxlv nhjfmeb |
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(14.4) |
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^_ k=1, 2, 3, ...- ghf_jLl_jZpL€ |
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,l_jZpL€ aZdLgqmxlv ijb ^hky]g_ggLmfh\b |
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PD[ = |
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(14.5) |
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^_ ε - ijbimklbfZ ihob[dZ j_amevlZlL\ |
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>hklZlgLmfh\b a[L`ghklL Ll_jZpLcgh]h ijhp_km fZxlv \b]ey^ |
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<1. |
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M= |
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<hgb ih\bggL\bdhgm\Zlbky ^ey mkLo agZq_gv i (i=1, 2, ..., n). |
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F_lh^ A_c^_ey |
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F_lh^ A_c^_ey \L^jLagy}lky \L^ f_lh^Z a\bqZcgboLl_jZpLc lLevdb nhjfmeZfb |
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mlhqg_ggy dhj_gL\ |
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(14.6) |
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M [LevrhklL \biZ^dL\ \Lg aZ[_ai_qm} [Levr kdhjm a[L`gLklv Ll_jZpLcgh]h ijhp_km
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F_lh^ GvxlhgZ F_lh^ GvxlhgZ } ihoL^gbf \L^ f_lh^m ^hlbqgbo ^ey h^gh]h jL\gyggy
<_dlhj ijbjhs_gv dhj_gL\ |
∆ X gZ dh`ghfm djhpL Ll_jZpLcgh]h ijhp_km |
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a¶ykh\m}lvky reyohf jLr_ggy kbkl_fb n eLg•cgbo jL\gygv a n g_\L^hfbfb |
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W[k-1]*∆ X=-F(X[k-1]), |
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(14.7) |
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∂I ( ; ) |
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(14.8) |
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– fZljbpy Ydh[• F(X) – \_dlhj e•\bo qZklbg ihqZldh\h€ kLkl_fb jL\gygv |
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Mlhqg_ggy dhj_gL\ a^Lckgxxlv aZ nhjfmehx |
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X[k]=X[k-1]+∆ X. |
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(14.9) |
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,l_jZpL€ aZ\_jrmxlv ijb a^Lckg_ggL mfh\b >ey `hjkldLrh]h dhgljh- |
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ex lj_[Z jZahf a mfh\hx i_j_\Ljylb mfh\m |
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(14.10) |
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AZ\^Zggy Jha\¶yaZlb kbkl_fm jL\gygv a gZqZevgbfb gZ[eb`_ggyfb a lZ[ebpL
F_lh^bqgLj_dhf_g^ZpL€
GZqZevg• gZ[eb`_ggy dhj_g•\ O0 fh`gZ \bagZqblb \•amZevgh ih[m^m\Z\rb ]jZn•db nmgdp•€ F(x) m ljbf•jghfm ijhklhj• lZ dhglmjg• e•g•€ gmevh\h]h j•\gx >ey pvh]h m iZd_l•0/} nmgdp•€ surf, mesh, contour.
surf(X, Y, Z, C) – [m^m} gZ _djZg• kiehrgm ih\_jogx a j_[jZfb ^ey agZq_gv fZkb\Z Z ydbc \bagZq_g gZ qbke_gg•kl• agZq_gv fZkb\•\ X • Y Dhe•j qZjmgdb \bagZqZ}lvky fZkb\hf K.
mesh(X, Y, Z, C) – [m^m} gZ _djZg• k•lqZlm ih\_jogx ^ey agZq_gv fZkb\Z Z,
61
ydbc \bagZq_g gZ qbke_gg•kl• agZq_gv fZkb\•\ X • Y Dhehj \mae•\ \bagZqZ}lvky fZkb\hf K Ydsh \•^kmlg•c Zj]mf_gl K lh dhe•j m pvhfm \biZ^dm af•gx}lvky ijhihj-p•cgh \bkhl• ih\_jog• C=Z Ydsh \•^kmlg• Zj]mf_glb X lZ Y lh X=1:n,
Y=1:m ^_>m, n]=size(Z).
contour(X, Y, Z, V) – jbkm} e•g•€ j•\gy ^ey fZkb\Z ^Zggbo Z \jZoh\mxqb ^•ZiZahg af•gb dhhj^bgZl X • Y ^ey aZ\^Zgbo agZq_gv yd• f•klylvky m \_dlhj• V.
IhagZqblb m ihqZldh\Lc kbkl_fL jL\gygv afLggL h^gbf Lf¶yf a jLagbfb ig^_dkZfb I_j_\Ljblb qb a^Lckgxxlvky mfh\b a[L`ghklLijb aZ\^Zggbo gZqZevgbo gZ[eb`_ggyo
Ijb jha\¶yam\ZggL kbkl_fb g_eLg•cgbo jL\gygv f_lh^hf GvxlhgZ lj_[Z kdeZklb nmgdp•€ ^ey jhajZomgdm fZljbp• Ydh[L jha\¶yam\Zggy kbkl_fb eLg•cgbo jL\gygv jha\¶yam\Zggy kbkl_fb g_eLg•cgbo jL\gygv
Ijb jha\¶yam\ZggL kbkl_fb f_lh^Zfb A_c^_ey L ijhklbo Ll_jZpLc lj_[Z
kdeZklb nmgdp•x ^ey jhajZomgdm ϕ 1 ... ϕ |
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LZ[ebpy |
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‹ \Zj |
Kbkl_fZ jL\gygv |
F_lh^ j•r_ggy |
GZq gZ[eb`_ggy |
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1 |
2x+tg(xy)=0 |
IjhklboLl_jZpLc |
x0=3 |
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(y2-7,5)2-15x=0 |
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y0=0 |
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2 |
tg(x)-cos(1,5y)=0 |
A_c^_ey |
x0=0 |
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2y3-x2-4x-3=0 |
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y0=1 |
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3 |
10x2+9y2-1=0 |
GvxlhgZ |
x0=0 |
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sin(3,2x+0,3y)+3x=0 |
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y0=0,5 |
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4 |
cos(y)+2x=0 |
A_c^_ey |
x0=0 |
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0,24x+3,5y+x2y=0 |
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y0=0 |
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5 |
sin(x+0,4)+3,5y-1,5=0 |
IjhklboLl_jZpLc |
x0=-1,3 |
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cos(y+0,2)+0,5x=0 |
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y0=0,5 |
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6 |
sin(3,3x-0,4y)+4x=0 |
GvxlhgZ |
x0=0 |
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8x2+25y2-1=0 |
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y0=0,5 |
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7 |
0,16x+2,1y+x2y=0 |
A_c^_ey |
x0=-1 |
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cos(y)+x=0 |
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y0=0 |
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8 |
2,1y3-x2-4x-3=0 |
L_` |
x0=0 |
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tg(2x)-cos(2y)=0 |
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y0=1 |
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9 |
(y2-7,5)2-15x=0 |
IjhklboLl_jZpLc |
x0=3 |
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tg(xy)+2x=0 |
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y0=0 |
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10 |
x2y+0,4x+5,3y=0 |
A_c^_ey |
x0=0 |
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4x+cos(y)=0 |
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y0=0 |
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62 |
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Ijh^h\`_ggy lZ[ebp• |
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‹ \Zj |
Kbkl_fZ jL\gygv |
F_lh^ j•r_ggy |
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GZq gZ[eb`_ggy |
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11 |
tg(xy)+6x=0 |
A_c^_ey |
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x0=3 |
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-120x+(y2-29)2=0 |
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y0=-0,5 |
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12 |
0,9x+cos(y+1,6)=0 |
IjhklboLl_jZpLc |
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x0=0,5 |
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0,1-2y+sin(x+1,8)=0 |
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y0=0,4 |
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13 |
cos(y+0,6)+0,6x=0 |
L_` |
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x0=-0,8 |
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sin(x+0,8)+2y-1=0 |
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y0=0,5 |
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14 |
tg(4x)-cos(3y)=0 |
A_c^_ey |
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x0=0 |
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2,3y3-x2-4x-3=0 |
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y0=1 |
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15 |
2,2y3-x2-4x-3=0 |
IjhklboLl_jZpLc |
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x0=0 |
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tg(3x)-cos(2,5y)=0 |
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y0=1 |
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16 |
5x+tg(xy)=0 |
GvxlhgZ |
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x0=0,6 |
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(y2-1,5)2-7,5x=0 |
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y0=-2 |
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17 |
0,5y-0,5+sin(x+1,2)=0 |
L_` |
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x0=-1 |
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0,7x+cos(y+0,8)=0 |
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y0=0 |
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18 |
sin(x+2,1)-3y+0,4=0 |
IjhklboLl_jZpLc |
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x0=0,4 |
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cos(y+1,8)+1,2x=0 |
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y0=0,5 |
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19 |
4,9y+0,32x+x2y=0 |
L_` |
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x0=0 |
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cos(y)+3x=0 |
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y0=0 |
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20 |
(y2-5)2-20x=0 |
GvxlhgZ |
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x0=0,3 |
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tg(xy)+4x=0 |
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y0=-2,8 |
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21 |
sin(4x-0,5y)+5x=0 |
GvxlhgZ |
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x0=0 |
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7x2+30y2-1=0 |
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y0=0,5 |
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22 |
tg(6x)-cos(4y)=0 |
IjhklboLl_jZpLc |
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x0=0 |
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2,5y3-x2-4x-3=0 |
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y0=1 |
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23 |
6x+tg(xy)=0 |
GvxlhgZ |
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x0=0,5 |
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(y2-2)2-12x=0 |
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y0=-2 |
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24 |
sin(3,1x+0,2y)+2x=0 |
L_` |
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x0=0 |
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12x2+5y2-1=0 |
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y0=0,5 |
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25 |
cos(y)+5x=0 |
A_c^_ey |
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x0=0 |
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0,48x+6,7y+x2y=0 |
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y0=0 |
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26 |
tg(5x)-cos(3,5y)=0 |
L_` |
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x0=0 |
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2,4y3-x2-3-4x=0 |
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y0=1 |
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27 |
12x2+5y2-1=0 |
GvxlhgZ |
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x0=0 |
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sin(3x+0,1y)+x=0 |
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y0=0,5 |
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28 |
0,6x+7,5y+x2y=0 |
IjhklboLl_jZpLc |
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x0=0 |
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cos(y)+6x=0 |
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y0=0 |
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29 |
sin(x+1,6)-y=0 |
L_` |
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x0=0,5 |
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cos(y+1,2)+0,8x=0 |
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y0=0,8 |
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30 |
4x2+35y2-1=0 |
GvxlhgZ |
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x0=0 |
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sin(4,2x-0,6y)+6x=0 |
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y0=0,5 |
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63 |
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P•ev jh[hlb gZ\qblbky \bagZqZlb fZdkbfZevg_ lZ f•g•fZevg_ agZq_ggy nmgdp•€ gZ aZ^Zghfm •gl_j\Ze•
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GZ^Zgbc gb`q_ f_lh^ ^ha\hey} agZclb lhqdm _dklj_fmfZ nmgdp•€ f o gZ •gl_j\Ze• [a‚b] >ey \bagZq_ggy ihrmdZ \•^j•ahd [a‚b] ih\bg_g fZlb h^bg fZdkbfmf Z[h f•g•fmf ^hke•^`m}fh€ nmgdp•€
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Ijbqhfm lhqdZ x1 \ k\hx q_j]m kl\hjx} ahehlbc i_j_j•a \•^j•adm [a‚x2], Z
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64
- ydsh f(x1)>f(x2) af•gx}fh e•\m f_`m •gl_j\ZeZ a=x1 •gZdr_ - ijZ\m b=x2 ; - ih\lhjx}fh ijhp_k kihqZldm a\Z`Zxqb sh h^gZ a lhqhd ahehlh]h i_j_j•am \`_
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- i•key aZ\_jr_ggy •l_jZp•c lhqdm f•g•fmfZ fh`gZ mlhqgblb ih^•eb\ \•^j•ahd
[a‚b] gZ\i•e xmin=(a+b)/2.
:gZeh]•qgbf aZkh[hf fh`gZ agZclb fZdkbfmf nmgdp•€ >ey agZoh^`_ggy f•g•fmfZ nmgdp•€ \ iZd_l• ML •kgmxlv nmgdp•€ fmin, fmins. min=fmin(Fun, x1, x2, Options, p1, p2, …) – h[qbkex} f•g•fmf nmgdp•€ f(x ydZ
aZibkZgZ m m–nZce• a •f’yf Fun gZ ^•ZiZahg• [x1, x2@Nmgdp•y f(x fh`_ [mlb hibkZgZ lZdh` yd kljhdh\Z af•ggZ
Options – \_dlhj hip•c yd• d_jmxlv ijhp_khf h[qbke_ggy lZ \b\h^m j_amevlZl•\g_h[h\ yadh\bc iZjZf_lj
p1, p2, …-\bdhjbklh\mxlv ydsh nmgdp•y fZ} [•evr h^gh]h Zj]mf_glZ f(x, p1, p2, …).
MIN=fmins(Fun, X0, Options, p1, p2, …) – f•g•fmf nmgdp•€ d•evdho af•ggbo
MIN − \_dlhj ydbc \•^ih\•^Z} dhhj^bgZlZf f•g•fmf•\ nmgdp•€ ih[ebam lhqhd sh \bagZqZxlvky \_dlhjhf X0.
AZ\^Zggy
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LZ[ebpy 5.1 |
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H VLQ [ |
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3,4 cos (0,5 x − 0,28) − |
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cos( 2 x ) |
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ln |
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ln (x / 2) cos( |
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66
Ijh^h\`_ggy lZ[ebp•
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[ + VLQ [ − |
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28 |
tg(x)+x |
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x cos(x / 3) |
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HVLQ[ + [ |
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67
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EZ[hjZlhjgZ jh[hlZ ‹ HI?J:PI2 A F:LJBPYFB«««««««………3
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68