Учёба / lab_mat-met

dh_nLpL}glL\ A lZ B fh`_ fZlb \b]ey^

function C=polysum(A,B)

n=length(A);

m=length(B);

if n>m, r=n-m; B=[zeros(1,r),B];

elseif m>n, r=m-n; A=[zeros(1,r),A];

end

C=A+B;

% end polysum

>ey \bdhgZggy [ievr kdeZ^gbo hi_jZpic ML fZ} \kljh}gi nmgdpi€ conv,

deconv, polyder lZ •gr•

C = conv(A, B) – h[qbkex} dh_n•p•}glb klmi•g_\h]h ihe•ghfZ ydbc } ^h[mldhf ^\ho ihe•ghf•\ a \_dlhjZfb dh_n•p•}gl•\ : • < Jhaf•j \_dlhjZ K \bagZqZ}lvky gZklmigbf qbghf

length(C)= length(A) + length(B) - 1.

[D, R] = deconv(A, B) – hi_jZp•y jhadeZ^m, h[qbkex}:

D – dh_n•p•}glb klmi•g_\h]h ihe•ghfZ hljbfZgh]h \•^ ^•e_ggy ihe•ghfZ a \_dlhjhf dh_n•p•}gl•\ : gZ ihe•ghf a \_dlhjhf dh_n•p•}gl•\ <;

R – hklZqZ \•^ ^•e_ggy Ijb pvhfm kijZ\_^eb\_ \•^ghr_ggy

A = conv(D, B) + R.

A1 = polyder(A) – h[qbkex} dh_n•p•}glb :1 klmi•g_\h]h ihe•ghfZ, ydbc } iho•^ghx ihe•ghfZ a dh_n•p•}glZfb :.

[Q, D] = polyder(A, B) – h[qbkex} qbk_evgbd Q • agZf_ggbd D iho•^gh€

ijbkmlg•c h^bg \bo•^gbc iZjZf_lj:

D = polyder(A, B) – h[qbkex} dh_n•p•}glb D iho•^gh€ \•^ ^h[mldZ ihe•ghf•\ a \_dlhjZfb dh_n•p•}gl•\ : • <, lh[lh D=(A•B)'.

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AZ\^Zggy

JhajZom\Zlb agZq_ggy afigghi Z ijb x ydbc afigx}lvky \i^ - ^h a djhdhf

0.1.

<bjZab ^ey \bjZom\Zggy Z gZ\_^_gi m lZ[ebpi < pbo \bjZaZo nmgdpi€ f1(x), f2(x), f3(x } klmi•g_\i ihe•ghfb ydi jiagylvky h^bg \i^ h^gh]h ihjy^dhf i agZq_ggyf dh_nipi}gli\

>ey g_iZjgbo \ZjiZgli\

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EZ[hjZlhjgZ jh[hlZ ‹

:IJHDKBF:P,Y F?LH>HF G:CF?GVRBO D<:>J:L,<

P•ev jh[hlb gZ\qblbky hibkm\Zlb lZ[ebqg• nmgdp•€ ZgZe•lbqgbfb \bjZaZfb

lh aZ^ZqZ a\h^blvky ^h \bagZq_ggy \_dlhjm dh_n•p•}gl•\ K=(K0, C1, …, Ck reyohf \bj•r_ggy kbkl_fb e•g•cgbo j•\gygv d 1)-]h ihjy^dm

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^_ m=0, 1, …, k; j=0, 1, …, k.

I•key \bagZq_ggy dh_n•p•}gl•\ kbkl_fm fh`gZ \bj•rblb [m^v-ydbf a \•^hfbo f_lh^•\ gZijbdeZ^ f_lh^hf =ZmkZ

:ijhdkbfZp•x f_lh^hf gZcf_gvrbo d\Z^jZl•\ qZklh aZklhkh\mxlv ^ey \bj•\gx\Zggy lZ[ebqg•o nmgdp•c sh [meb ihemq_g• \ oh^• _dki_jbf_glZ Z lZdh` ^ey af_gr_ggy h[¶}fm •gnhjfZp•€ ijh lZ[ebqg• nmgdp•€ ijb g_\bkhdbo \bfh]Zo ^h lhqghkl• jhajZomgdm

< ML ^ey agZoh^`_ggy dh_n•p•}gl•\ Zijhdkbfmxqh€ nmgdp•€ f_lh^hf gZcf_gvrbo d\Z^jZl•\ \bdhjbklh\m}lvky nmgdp•y polyfit:

P=polyfit(Xt, Yt, k).

P – \_dlhj-jy^hd dh_n•p•}gl•\ Zijhdkbfmxqh]h ihe•ghfZ mihjy^dh\Zgbc aZ m[m\Zggyf klmi•g_c x ;

Yt (Xt) – lZ[ebqgZ nmgdp•y

k – ihjy^hd Zijhdkbfmxqh]h ihe•ghfZ

AZ\^Zggy

:ijhdkbfm\Zlb lZ[ebqgm nmgdp•x sh ijb\_^_gZ \ lZ[ebp• KI k-]h ihjy^dm f_lh^hf gZcf_gvrbo d\Z^jZl•\ k=2, 3, 4, n- H[qbkeblb agZq_ggy f•g•f•amxqh]h nmgdp•hgZem Φ Ijh•eexkljm\Zlb j_amevlZlb ]jZn•dZfb <bdhgZlb ijh]jZfm ^\•q• ijb j•ag•c d•evdhkl• lZ[ebqgbo lhqhd n lZ n Hp•gblb \ieb\ d•evdhkl• lhqhd gZ lhqg•klv ZijhdkbfZp•€

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24

EZ[hjZlhjgZ jh[hlZ ‹

1GL?JIHEYP1Y

P•ev jh[hlb gZ\qblbky \bagZqZlb agZq_ggy nmgdp•c sh aZ^Zg• lZ[ebqgh ijb [m^v-ydbo agZq_ggyo Zj]mf_gl•\ aZ ^hihfh]hx •gl_jiheyp•€ nmgdp•c klmi•g_\bf ihe•ghfhf KI

L_hj_lbqg• \•^hfhkl•

M gZmp• • l_ogbp• [Z]Zlh yd• nmgdp•hgZevg• aZe_`ghkl• aZ^Zxlvky g_ ZgZe•lbqgh Z m \b]ey^• ]jZn•d•\ qb lZ[ebpv

M ?HF •gnhjfZp•y ijh lZd• nmgdp•€ a[_j•]Z}lvky m \b]ey^• fZkb\•\ gZijbdeZ^

Px aZ^Zqm fh`eb\h \bj•rblb \•^rmdZ\rb nmgdp•x sh •gl_jihex} F(x). <hgZ ijbcfZ} gZ ^_ydhfm •gl_j\Ze• > [ M [ M+ N @ agZq_ggy sh ki•\iZ^Zxlv a• agZq_ggyfb lZ[ebqgh€ nmgdp•€ m \maeh\bo lhqdZo

) ([ M ) = \ M )([ M+ ) = \ M+ ) ([ M+ N ) = \ M+ N

Lhqdm [ M a\mlv ihqZldh\bc \ma_e •gl_jiheyp•€

>m`_ qZklh \ ydhkl• nmgdp•€ sh •gl_jihex} \bdhjbklh\mxlv Ze]_[jZ•qgbc ihe•ghf

Ijb k=n ihe•ghf Pk(x klZ} ]eh[Zevgbf •gl_jiheyglhf [h \ pvhfm \biZ^dm ch]h agZq_ggy ki•\iZ^Zxlv a• agZq_ggyfb ihqZldh\h€ nmgdp•€ \ mk•o \maeZo.

Ydsh lZ[ebqgZ nmgdp•y aZ^ZgZ m j•\ghf•jgh jhalZrh\Zgbo \maeZo lh[lh

[L + − [L = K = FRQVW lh agZq_ggy y(x) fh`gZ \bagZqblb ih i_jr•c bgl_jiheyp•cg•c nhjfme• GvxlhgZ

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[ [ M [ M + N @ Ze_ gZc[•evrm lhqg•klv \hgb aZ[_ai_qmxlv ih[ebam ihqZldh\h]h \maeZ •gl_jiheyp•€ [ M : [ >[ M [ M + @

Lhfm i_j_^ lbf yd \bdhjbklh\m\Zlb •gl_jiheyp•cg• nhjfmeb g_h[o•^gh agZclb ghf_j ihqZldh\h]h \maeZ •gl_jiheyp•€ Mfh\m \b[hjm fh`gZ ah[jZablb

M k_j_^h\bs• ML p_c ihrmd fh`_ aZ[_ai_qblb ihke•^h\g•klv ^•c

jv = find( xt<x );

if isempty( jv ), j=1;

else j = max( jv );

end

^_ xt – Zj]mf_gl lZ[ebqgh€ nmgdp•€ \_dlhj x – lhqdZ •gl_jihex\Zggy

M l_og•qgbo jhajZomgdZo a\bqZcgh aZklhkh\mxlv e•g•cgm Z[h d\Z^jZlbqgm •gl_jiheyp•x M lZdhfm \biZ^dm nhjfmeb lZ ijbcfZxlv gZklmigbc \b]ey^

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Nhjfmeb lZ y\eyxlv kh[hx j•\gyggy ijyfh€ ydZ ijhoh^blv q_j_a lhqdb [ M \ M ([ M+ \ M+ ) Z lZ - j•\gyggy d\Z^jZlbqgh€ iZjZ[heb ydZ ijhoh^blv q_j_a lhqdb ([ M \ M ) ([ M+ \ M+ ) ([ M+ \ M+ )

>ey •gl_jihex\Zggy lZ[ebqgh€ nmgdp•€ \ iZd_l• ML \bdhjbklh\mxlvky interp1, interp2, icubic, splin_ lZ ^_yd• •gr•

Y=interp1(Xt, Yt, X, metod),

Yt(Xt) – lZ[ebqgZ nmgdp•y

X – lhqdZ Z[h fZkb\ lhqhd m ydbo g_h[o•^gh h[qbkeblb agZq_ggy •gl_jihexxqh€ nmgdp•€

metod – f_lh^ •gl_jihex\Zggy fh`_ ijbcfZlb gZklmig• agZq_ggy ‘linear’ – e•gLcgZ •gl_jiheyp•y

‘cubic’ – dm[•qgZ •gl_jiheyp•y ‘spline’ – dm[•qgZ kieZcg-•gl_jiheyp•y

'nearest' – •gl_jiheyp•y aZ gZc[eb`qbf kmk•^g•f \maehf •kgm} ihqbgZxqb a

ML5.3 ).

Y=icubic(Xt, Yt, X) – dm[•qgZ •gl_jiheyp•y

Y=spline(Xt, Yt, X) – dm[•qgZ kieZcg-•gl_jiheyp•y

27

AZ\^Zggy

JhajZom\Zlb ijb[ebag• agZq_ggy lZ[ebqgbo nmgdp•c yd• aZ\^Zg• m lZ[ebp•

^ey Zj]mf_gl•\ dhlj• af•gxxlvky \•^ xmin ^h xmax \ lhqdZo

F_lh^bqg• j_dhf_g^Zp•€ I•key ihrmdm ghf_jZ ihqZldh\h]h \maeZ •gl_jiheyp•€ i_j_\•jl_ mfh\m [ = [ M .

Ijb €€ \bdhgZgg• g_ \bdhjbklh\mcl_ •gl_jiheyp•cgm nhjfmem Z agZoh^vl_ agZq_ggy [_aihk_j_^gvh •a lZ[ebp• \ = \L .

>ey ]jZn•qgh€ i_j_\•jdb \b\_^•lv gZ _djZg m ]jZn•qghfm j_`bf• lZ[ebqgm nmgdp•x • €€ •gl_jihevh\Zg• agZq_ggy m j•ag•c nhjf• qb j•agbf dhevhjhf GZijbdeZ^ nmgdp•x \b\_^•lv gZ _djZg m \b]ey^•³a•jhd´Z •gl_jihevh\Zg• agZq_ggy – m \b]ey^• \•^j•ad•\ ijyfbo f•` ^\hfZ kmk•^g•fb lhqdZfb

<b[•j f_lh^Z •gl_jihex\Zggy hj]Zg•am\Zlb m \b]ey^• f_gx >ey pvh]h \bdhjbklm\Zlb nmgdp•x ML menu.

EZ[hjZlhjgZ jh[hlZ ‹

G?E1G1CGBC I:JGBC J?=J?K1CGBC :G:E1A

P•ev jh[hlb gZ\qblbky hibkm\Zlb lZ[ebqg• nmgdp•€ ZgZe•lbqgbfb g_e•g•c- gbfb \bjZaZfb

L_hj_lbqg• \•^hfhkl•

:ijhdkbfZp•x lZ[ebqgh€ nmgdp•€ yi=f(xi), i=1, 2, … , n f_lh^hf gZcf_gvrbo d\Z^jZl•\ gZab\Zxlv j_]j_k•cgbf ZgZe•ahf

E•g•cgbc j_]j_k•cgbc ZgZe•a ihey]Z} m \bagZq_gg• iZjb dh_n•p•}gl•\ C1 • C2 e•g•cgh€ aZe_`ghkl•

G_e•g•cgZ iZjgZ j_]j_k•y ihey]Z} m \bagZq_gg• iZjb dh_n•p•}gl•\ d1 • d2

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AZ\^Zggy

:ijhdkbfm\Zlb lZ[ebqgm nmgdp•x sh ijb\_^_gZ m lZ[ebp• g_e•g•cghx nmgdpb}x yZ(x H[qbkeblb agZq_ggy f•g•f•amxqh]h nmgdp•hgZem Ijh•exkljm\Zlb j_amevlZlb ]jZn•dZfb

<bo•^g• ^Zgg•

n=4; x1=1; x2=2; x3=3,5; x4=5.

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