octave:2> A=toeplitz([-2 1 0 0]) A = -2 1 0 0 1 -2 1 0 0 1 -2 1 0 0 1 -2 octave:3> eig(A) ans = -3.61803 -2.61803 -1.38197 -0.38197 octave:4> potenzefailed(A,tol,100) error: `tol' undefined near line 4 column 17 error: evaluating argument list element number 2 octave:4> potenzefailed(A,1e-6,100) x = 3 4 4 3 ans = -2.6180 octave:5> [lambda,y,iter]=potenzefailed(A,1e-6,100) x = 3 4 4 3 lambda = -2.6180 y = 0.60150 -0.37175 -0.37175 0.60150 iter = 8 octave:6> [lambda,y,iter]=potenzefailed(A,1e-10,100) x = 3 4 4 3 lambda = -2.6180 y = 0.60150 -0.37175 -0.37175 0.60150 iter = 10 octave:7> [lambda,y,iter]=potenzefailed(A,1e-14,100) x = 3 4 4 3 lambda = -2.6180 y = 0.60150 -0.37175 -0.37175 0.60150 iter = 12 octave:8> [lambda,y,iter]=potenzefailed(A,1e-16,100) x = 3 4 4 3 lambda = -2.6180 y = -0.60150 0.37175 0.37175 -0.60150 iter = 13 octave:9> [lambda,y,iter]=potenzefailed(A,0,100) x = 3 4 4 3 lambda = -2.6180 y = -0.60150 0.37175 0.37175 -0.60150 iter = 13 octave:10> normest(A) ans = 3.6180 octave:11> A A = -2 1 0 0 1 -2 1 0 0 1 -2 1 0 0 1 -2 octave:12> eig(A) ans = -3.61803 -2.61803 -1.38197 -0.38197 octave:13> [V,D]=eig(A) V = 0.37175 -0.60150 -0.60150 -0.37175 -0.60150 0.37175 -0.37175 -0.60150 0.60150 0.37175 0.37175 -0.60150 -0.37175 -0.60150 0.60150 -0.37175 D = -3.61803 0.00000 0.00000 0.00000 0.00000 -2.61803 0.00000 0.00000 0.00000 0.00000 -1.38197 0.00000 0.00000 0.00000 0.00000 -0.38197 octave:14> A*V(:,1) ans = -1.3450 2.1763 -2.1763 1.3450 octave:15> D(1,1)*V(:,1) ans = -1.3450 2.1763 -2.1763 1.3450 octave:16> A*V ans = -1.34500 1.57475 0.83125 0.14200 2.17625 -0.97325 0.51374 0.22975 -2.17625 -0.97325 -0.51374 0.22975 1.34500 1.57475 -0.83125 0.14200 octave:17> D*V ans = -1.34500 2.17625 2.17625 1.34500 1.57475 -0.97325 0.97325 1.57475 -0.83125 -0.51374 -0.51374 0.83125 0.14200 0.22975 -0.22975 0.14200 octave:18> V*D ans = -1.34500 1.57475 0.83125 0.14200 2.17625 -0.97325 0.51374 0.22975 -2.17625 -0.97325 -0.51374 0.22975 1.34500 1.57475 -0.83125 0.14200 octave:19> A*V ans = -1.34500 1.57475 0.83125 0.14200 2.17625 -0.97325 0.51374 0.22975 -2.17625 -0.97325 -0.51374 0.22975 1.34500 1.57475 -0.83125 0.14200 octave:20> A*V(:,1) ans = -1.3450 2.1763 -2.1763 1.3450 octave:21> V(:,1)*D(1,1) ans = -1.3450 2.1763 -2.1763 1.3450 octave:22> norm(A*V(:,1)-V(:,1)*D(1,1)) ans = 2.2204e-16 octave:23> eps ans = 2.2204e-16 octave:24> A=rand(100); octave:25> [V,D]=eig(A); octave:26> norm(A*V-V*D) ans = 5.7868e-14 octave:27> quit