Example of accelerated QR method - Matrix tridiagonal The acceleration uses a shift based on the lower right-hand element a = 5 4 0 4 3 2 0 2 1 iteration = 1 q = -0.70710678118655 0.40824829046386 -0.57735026918963 -0.70710678118655 -0.40824829046386 0.57735026918963 0 0.81649658092773 0.57735026918963 r = -5.65685424949238 -4.24264068711928 -1.41421356237310 0 2.44948974278318 -0.81649658092773 0 0 1.15470053837925 a = 8.00000000000000 -1.73205080756888 0.00000000000000 -1.73205080756888 -0.66666666666667 0.94280904158206 0 0.94280904158206 1.66666666666667 iteration = 2 q = -0.96457885687694 -0.24912355419337 0.08674723979494 0.26379467179225 -0.91093315680847 0.31719576756473 0 0.32884379053438 0.94438432929977 r = -6.56590520119740 1.05517868716899 0.24870800168690 0 2.86704225142876 -0.85883601651591 0 0 0.29905503761159 a = 8.27835051546392 0.75631046973015 0.00000000000000 0.75631046973015 -1.22744007324913 0.09834239214660 0 0.09834239214660 1.94908955778521 iteration = 3 q = -0.99293611762032 0.11859569613299 -0.00359543930771 -0.11865018468205 -0.99248012466506 0.03008879890834 0 0.03030285470978 0.99954076304893 r = -6.37428817963382 -0.37407215415923 -0.01166834299027 0 3.24531774608256 -0.09760286961752 0 0 0.00295900446146 a = 8.32273424563932 -0.38505754992463 0.00000000000000 -0.38505754992463 -1.27478144900181 0.00008966628228 0 0.00008966628228 1.95204720336249 iteration = 4 q = -0.99817836736413 -0.06033197264715 0.00000166752172 0.06033197267019 -0.99817836698287 0.00002758875664 0 0.00002763910494 0.99999999961804 r = -6.38231327242622 0.18967517845916 0.00000540974369 0 3.24418183879845 -0.00008950294322 0 0 0.00000000247378 a = 8.33417772332233 0.19572789003552 0.00000000000000 0.19572789003552 -1.28622492915860 0.00000000000007 0 0.00000000000007 1.95204720583627 iteration = 5 q = -0.99953006493600 0.03065369943485 0.00000000000000 -0.03065369943485 -0.99953006493600 0.00000000000002 0 0.00000000000002 1.00000000000000 r = -6.38513111448502 -0.09637088992261 0.00000000000000 0 3.24275014128402 -0.00000000000007 0 0 0.00000000000000 a = 8.33713184761629 -0.09940228817323 0.00000000000000 -0.09940228817323 -1.28917905345256 0.00000000000000 0 0.00000000000000 1.95204720583627