TEME Cna - TEME Cna 1.function[X]=lip_inf_biddiag(A,C)...

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TEME Cna 1.function[X]=lip_inf_biddiag(A,C) [n]=size(A); for i=n:-1:1 for j=n:-1:1 X(i,j)=C(i,j)-A(i,i+1)*X(i+1,j)-X(i,j+1)*A(i+1,j); end end 2. function[X]=lip_inf_triungh(A,C) [n]=size(A); for i=n:-1:1 for j=n:-1:1 a=0; for k=i+1:n a=a+A(i,k)*X(k,j); end b=0; for k=i+1:n b=b+X(i,k)*A(k,j); end X(i,j)=(C(i,j)-a-b)/(A(i,i)+A(i,j)); end end 3. function[X]=sylv(A,B,C) [n]=size(C); for i=n:-1:1 for j=n:-1:1 a=0; for k=i+1:n a=a+A(i,k)*X(k,j); end b=0; for k=j+1:n b=b+X(i,k)*B(k,j); end X(i,j)=(C(i,j)-a-b)/(A(i,i)+B(j,j));
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end end 4. function[X]=sylv_inf(A,B,C) [n]=size(A); for i=n:-1:1 for j=1:n a=0; for k=1:i-1 a=a+A(i,k)*X(k,j); end b=0; for k=j+1:n b=b+X(i,k)*B(k,j); end X(i,j)=(C(i,j)-a-b)/(A(i,i)+B(j,j)); end end 1.Se considera matricea: - - - - = 0 3 1 2 5 1 2 3 3 A . Sa se calculeze « de mana« fara a folosi functii Matlab : Comparati rezultatele obtinute cu cele date prin aplicarea functiilor Matlab corespunzatoare a) detA= -6+(-6)-[-10-18]=16 - - - - - = 0 2 2 3 5 3 1 1 3 T A iar - - = 12 6 2 4 2 2 4 6 6 * A ) 8 cos( ) ) ) 2 ln 1 A H c e G b A F a A π = = = -
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- - - - = = - 12 6 2 4 2 2 4 6 6 16 1 * det 1 1 A A A In Matlab >> F=A^(-1) sau F=inv(A) b) 2 ln A e G = X e G A X = - - - - = - - - - = = 0 2 ln 3 2 ln 2 ln 2 2 ln 5 2 ln 2 ln 2 2 ln 3 2 ln 3 2 ln 0 3 1 2 5 1 2 3 3 2 ln Pentru determinarea valorii lui X se foloseste un algorim(algoritmul 3.1) in care matricea X este descompusa in vectori si valorii proprii. In Matlab >> [G]=alg31('exp',A*log(2)) unde algoritmul de calcul este urmatorul : function [G]=alg31(f,A) [n,n]=size(A); [V,L]=eig(A); D=zeros(n,n); for i=1:n D(i,i)=feval(f,L(i,i)); end G=V*D/V; G=real(F); c) = A H 8 cos π Y e H A Y = - - - - = - - - - = = 0 8 3 8 8 2 8 5 8 8 2 8 3 8 3 8 0 3 1 2 5 1 2 3 3 8 In Matlab: (prin aplicarea aceluiasi algoritm se obtine): >> [H]=alg31('cos',A*pi/8) 2.Este adevarata urmatoarea afirmatie: Daca AB=BA atunci B A B A e e e = +
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Argumentati. Egalitatea este adevarata in pe baza propozitiilor:
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This note was uploaded on 11/05/2011 for the course AUTOMATIC 18 taught by Professor Corneliupopeea during the Spring '11 term at UPB Colombia.

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TEME Cna - TEME Cna 1.function[X]=lip_inf_biddiag(A,C)...

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