Example of unaccelerated QR method: Matrix tridiagonal a = 5 4 0 4 3 2 0 2 1 iteration = 1 q = -0.78086880944303 0.04863244349441 -0.62279915532922 -0.62469504755442 -0.06079055436801 0.77849894416152 0 0.99696509163531 0.07784989441615 r = -6.40312423743285 -4.99756038043539 -1.24939009510885 0 2.00608829414421 0.87538398289929 0 0 1.63484778273920 a = 8.12195121951219 -1.25319342230879 0.00000000000000 -1.25319342230879 0.75077605321508 1.62988616952836 0 1.62988616952836 0.12727272727273 iteration = 2 q = -0.98830462391350 -0.04882800076470 -0.14446382485768 0.15249252555843 -0.31645445411499 -0.93627058488430 0 -0.94735020177974 0.32019930541445 r = -8.21806457542490 1.35302459040932 0.24854545836413 0 -1.72046848828066 -0.63635658191055 0 0 -1.48526183836823 a = 8.32827735644637 -0.26235858492161 0.00000000000000 -0.26235858492161 1.14730245255772 1.40706310227388 0 1.40706310227388 -0.47557980900409 iteration = 3 q = -0.99950417649593 -0.01980518728009 -0.02447765764909 0.03148652358050 -0.62869333135892 -0.77701563300724 0 -0.77740108673813 0.62900520692469 r = -8.33240876055534 0.29835306709514 0.04430352554900 0 -1.80995772488270 -0.51489492885029 0 0 -1.39245220326629 a = 8.33767145732878 -0.05698927658423 0.00000000000000 -0.05698927658423 1.53818822891948 1.08249385605011 0 1.08249385605011 -0.87585968624826 iteration = 4 q = -0.99997664114668 -0.00558907948288 -0.00393438070620 0.00683499531875 -0.81769608723308 -0.57560958275788 0 -0.57562302865177 0.81771518812222 r = -8.33786622032283 0.06750145472409 0.00739884043867 0 -1.88056037053545 -0.38098598527382 0 0 -1.33929760492814 a = 8.33813282945582 -0.01285362132923 0.00000000000000 -0.01285362132923 1.75703116350963 0.77093054361480 0 0.77093054361480 -1.09516399296545 iteration = 5 q = -0.99999881181897 -0.00141163628021 -0.00061938974870 0.00154154489017 -0.91572721101678 -0.40179758416743 0 -0.40179806157627 0.91572829906777 r = -8.33814273667885 0.01556214846877 0.00118842404019 0 -1.91870150042640 -0.26592730711039 0 0 -1.31263069046384 a = 8.33815681920628 -0.00295776449374 0.00000000000000 -0.00295776449374 1.86385625027633 0.52741246699388 0 0.52741246699388 -1.20201306948260 iteration = 6 q = -0.99999993708459 -0.00034132437698 -0.00009658408171 0.00035472639479 -0.96221865787031 -0.27227766822756 0 -0.27227768535802 0.96221871840870 r = -8.33815734380486 0.00361892331572 0.00018708712298 0 -1.93703889578902 -0.18020477980612 0 0 -1.30020211193530 a = 8.33815810293390 -0.00068711882407 0.00000000000000 -0.00068711882407 1.91292070688477 0.35401602153535 0 0.35401602153535 -1.25107880981866 iteration = 7 q = -0.99999999660458 -0.00008103060803 -0.00001499598719 0.00008240654750 -0.98330302895180 -0.18197567547170 0 -0.18197567608959 0.98330303229052 r = -8.33815813124544 0.00084475601282 0.00002917323809 0 -1.94540297441219 -0.12043911401507 0 0 -1.29461189197581 a = 8.33815817254733 -0.00016031394261 0.00000000000000 -0.00016031394261 1.93483762647186 0.23558787431592 0 0.23558787431592 -1.27299579901919 iteration = 8 q = -0.99999999981517 -0.00001908558276 -0.00000232388073 0.00001922654131 -0.99266854311063 -0.12086837116866 0 -0.12086837119100 0.99266854329410 r = -8.33815817408847 0.00019751417814 0.00000452954000 0 -1.94912756740668 -0.07999574321128 0 0 -1.29213800806754 a = 8.33815817634484 -0.00003747498170 0.00000000000000 -0.00003747498170 1.94450657785851 0.15617861638910 0 0.15617861638910 -1.28266475420335 iteration = 9 q = -0.99999999998990 -0.00000447996881 -0.00000035982153 0.00000449439563 -0.99679004244501 -0.08006004785337 0 -0.08006004785418 0.99679004245507 r = -8.33815817642905 0.00004621436357 0.00000070192849 0 -1.95076846161220 -0.05298708805710 0 0 -1.29105112229977 a = 8.33815817655254 -0.00000876752526 0.00000000000000 -0.00000876752526 1.94874872645631 0.10336161463352 0 0.10336161463352 -1.28690690300885 iteration = 10 q = -0.99999999999945 -0.00000105001830 -0.00000005569296 0.00000105149424 -0.99859634061476 -0.05296554077616 0 -0.05296554077619 0.99859634061531 r = -8.33815817655715 0.00001081662331 0.00000010868414 0 -1.95148795082229 -0.03505481008659 0 0 -1.29057512787178 a = 8.33815817656392 -0.00000205197833 0.00000000000000 -0.00000205197833 1.95060542341798 0.06835600956003 0 0.06835600956003 -1.28876359998190 iteration = 20 q = -1.00000000000000 -0.00000000000052 0.00000000000000 0.00000000000052 -0.99999964439928 -0.00084332752219 0 -0.00084332752219 0.99999964439928 r = -8.33815817656458 0.00000000000535 0.00000000000000 0 -1.95204706413938 -0.00055814942504 0 0 -1.29020547605539 a = 8.33815817656458 -0.00000000000101 0.00000000000000 -0.00000000000101 1.95204684069282 0.00108806578723 0 0.00108806578723 -1.29020501725740