expl A = -149 -50 -154 537 180 546 -27 -9 -25 [X, D] = eig(A) X = 0.3162 -0.4041 -0.1391 -0.9487 0.9091 0.9740 -0.0000 0.1010 -0.1789 D = 1.0000 0 0 0 2.0000 0 0 0 3.0000 u = X(:,1); w = [1 0 0]\X {Error using \ Matrix dimensions must agree.} w = [1 0 0]/X w = 411.0961 135.9779 420.5829 c = norm(u)*norm(w)/abs(w*u) c = 603.6390 A(1,1) = A(1,1)- 0.001; t = -0.001; E = [1 0 0; 0 0 0, 0 0 0]; {Error using vertcat Dimensions of arrays being concatenated are not consistent.} E = [1 0 0; 0 0 0; 0 0 0]; E E = 1 0 0 0 0 0 0 0 0 B = A +t*E; del = w *E*u/(w*u) del = 130.0000 ll = 1 + t*det {Error using det Not enough input arguments.} ll = 1 + t*del ll = 0.8700 eig(B) ans = 0.7827 2.1697 3.0456 eig(A) ans = 0.8825 2.0946 3.0219 expl A = -149 -50 -154 537 180 546 -27 -9 -25 B =A+t*E; eig(B) ans = 0.8825 2.0946 3.0219 expl A = -149 -50 -154 537 180 546 -27 -9 -25 powerit(A,20) iter 1 -> res= 7.0469e+02 alph= 6.8096e+02 iter 2 -> res= 6.8914e-01 alph= 3.5372e+00 iter 3 -> res= 1.4854e-01 alph= 2.8899e+00 iter 4 -> res= 7.4723e-02 alph= 2.7806e+00 iter 5 -> res= 7.2415e-02 alph= 2.7907e+00 iter 6 -> res= 6.3615e-02 alph= 2.8315e+00 iter 7 -> res= 5.0331e-02 alph= 2.8745e+00 iter 8 -> res= 3.7353e-02 alph= 2.9104e+00 iter 9 -> res= 2.6656e-02 alph= 2.9376e+00 iter 10 -> res= 1.8563e-02 alph= 2.9573e+00 iter 11 -> res= 1.2729e-02 alph= 2.9710e+00 iter 12 -> res= 8.6424e-03 alph= 2.9805e+00 iter 13 -> res= 5.8308e-03 alph= 2.9869e+00 iter 14 -> res= 3.9177e-03 alph= 2.9912e+00 iter 15 -> res= 2.6253e-03 alph= 2.9941e+00 iter 16 -> res= 1.7562e-03 alph= 2.9961e+00 iter 17 -> res= 1.1734e-03 alph= 2.9974e+00 iter 18 -> res= 7.8344e-04 alph= 2.9983e+00 iter 19 -> res= 5.2281e-04 alph= 2.9988e+00 iter 20 -> res= 3.4877e-04 alph= 2.9992e+00 ans = -0.1430 1.0000 -0.1835 eig(A) ans = 1.0000 2.0000 3.0000 A A = -149 -50 -154 537 180 546 -27 -9 -25 [Q, R] = qr(A); A = R*Q; [Q, R] = qr(A); A = R*Q; [Q, R] = qr(A); A = R*Q; A A = 2.7811 -13.8833 816.1534 -0.0807 1.6294 49.2437 -0.0013 0.0104 1.5895 A = R*Q; expl A = -149 -50 -154 537 180 546 -27 -9 -25 for i=1:10 [Q,R] = qr(A); A = R*Q; end A A = 2.9724 -7.9826 -805.2418 -0.0111 1.0450 -142.2851 0.0001 -0.0003 1.9827 expl A = -149 -50 -154 537 180 546 -27 -9 -25 qrs(A,6); A = 3.5329 -35.9345 816.9585 -0.0960 2.3618 2.5246 -0.0070 0.0996 0.1053 A = 2.8682 -18.9262 -817.1418 -0.0871 1.8819 -25.3913 0.0023 -0.0238 1.2499 A = 2.7067 -11.1315 814.7416 -0.0795 1.5184 69.2567 -0.0008 0.0050 1.7749 A = 2.9929 -8.2426 -805.9410 -0.0102 1.0420 -138.2541 0.0002 -0.0006 1.9651 A = 2.9534 -7.7434 804.5406 -0.0120 1.0477 146.2111 -0.0000 0.0000 1.9989 A = 3.0467 -7.7021 -802.6325 0.0124 0.9533 -156.3477 0.0000 -0.0000 2.0000 expl A = -149 -50 -154 537 180 546 -27 -9 -25 qrsd(A,10); ni = 3 ; shift = 2.718652e+00 B = 0.8129 2.7890 817.7500 -0.0988 2.4720 -0.2827 0.0002 -0.0037 2.7151 B = 0.8129 2.7890 817.7500 -0.0988 2.4720 -0.2827 0.0002 -0.0037 2.7151 ni = 3 ; shift = 2.467809e+00 B = 0.8567 19.3962 -816.0550 -0.0023 1.3149 48.9688 0.0002 -0.0275 3.8284 B = 0.8567 19.3962 -816.0550 -0.0023 1.3149 48.9688 0.0002 -0.0275 3.8284 ni = 3 ; shift = 2.091220e+00 B = 1.0277 -5.0364 816.1767 -0.0099 2.7910 -50.5337 0.0000 -0.0027 2.1813 B = 1.0277 -5.0364 816.1767 -0.0099 2.7910 -50.5337 0.0000 -0.0027 2.1813 ni = 3 ; shift = 2.007351e+00 B = 0.9648 -7.7295 -815.6055 0.0093 3.0369 58.7431 -0.0000 -0.0000 1.9984 B = 0.9648 -7.7295 -815.6055 0.0093 3.0369 58.7431 -0.0000 -0.0000 1.9984 ni = 3 ; shift = 2.000051e+00 B = 1.0341 -7.7231 816.0999 -0.0087 2.9659 -51.4243 0.0000 -0.0000 2.0000 B = 1.0341 -7.7231 816.0999 -0.0087 2.9659 -51.4243 0.0000 -0.0000 2.0000 ni = 3 ; shift = 2.000000e+00 B = 0.9648 -7.7052 -815.6054 0.0093 3.0352 58.7486 -0.0000 -0.0000 2.0000 B = 0.9648 -7.7052 -815.6054 0.0093 3.0352 58.7486 -0.0000 -0.0000 2.0000 *** deflating ni = 2 ; shift = 1.000000e+00 B = 3.0000 7.7145 -815.6054 -0.0000 1.0000 58.7486 -0.0000 -0.0000 2.0000 B = 3.0000 7.7145 803.5647 -0.0000 1.0000 -151.4837 -0.0000 -0.0000 2.0000 *** deflating diary off