MAT 581 HW (chp 6 and 8)

MAT 581 HW (chp 6 and 8) - H/W chap 6 & 8 P 6.2.4...

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P 6.2.4 M-Files function x = TriCorner1(d,e,f,alpha,beta,b) n = length(b); e_1 = zeros(n,1); e_1(1) = 1; e_n = zeros(n,1); e_n(n) = 1; [l,u] = TriDiLU(d,e,f); y = LBiDiSol(l,b); z = UBiDiSol(u,f,y); t = LBiDiSol(l,alpha*e_n); y1 = UBiDiSol(u,f,t); t = LBiDiSol(l,beta*e_1); y2 = UBiDiSol(u,f,t); Y = [y1 y2]; delta = 1/((1+Y(1,1))*(1+Y(n,2))-(Y(1,2))*(Y(n,1))); V(1,1) = 1+Y(n,2); V(1,2) = -Y(1,2); V(2,1) = -Y(n,1); V(2,2) = 1+Y(1,1); V = delta*V; s=[z(1); z(n)]; x=z-Y*V*s; W = diag(e(2:n),-1) + diag(d) + diag(f(1:n-1),1); T = W+alpha*e_n*e_1'+beta*e_1*e_n'; disp ( 'W=' );disp (W); disp ( 'T=' ); disp (T); function x = LBiDiSol(l,b) % x = LBiDiSol(l,b) % % Solves the n-by-n unit lower bidiagonal system Lx = b % where l and b are n-by-1 and L = I + diag(l(2:n),-1). n = length(b); x = zeros(n,1); x(1) = b(1); for i=2:n x(i) = b(i) - l(i)*x(i-1); end function x = UBiDiSol(u,f,b)
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% x = UBiDiSol(u,f,b) % % Solves the n-by-n nonsingular upper bidiagonal system Ux = b % where u, f, and b are n-by-1 and U = diag(u) + diag(f(1:n-1),1). n = length(b); x = zeros(n,1); x(n) = b(n)/u(n); for i=n-1:-1:1 x(i) = (b(i) - f(i)*x(i+1))/u(i); end Script d=[4 5 0 4 2 6]; e=[8 7 4 7 4 2]; f=[2 4 7 6 2 4]; b=[1 3 56 2 9 3]'; alpha = 4; beta = 8; x = TriCorner1(d,e,f,alpha,beta,b); Output W= 4 2 0 0 0 0 7 5 4 0 0 0 0 4 0 7 0 0 0 0 7 4 6 0 0 0 0 4 2 2 0 0 0 0 2 6 T= 4 2 0 0 0 8 7 5 4 0 0 0 0 4 0 7 0 0 0 0 7 4 6 0 0 0 0 4 2 2 4 0 0 0 2 6 P 6.3.5
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M-Files function x = ProdSolve(A,B,C,f) [LA,UA,pivA] = GEpiv(A); yA = LTriSolM(LA,f(pivA)); xA = UTriSol(UA,yA); [LB,UB,pivB] = GEpiv(B); yB = LTriSolM(LB,xA(pivB));
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MAT 581 HW (chp 6 and 8) - H/W chap 6 & 8 P 6.2.4...

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