Program illustrates standard Lanczos algorithm. The specific example generates a random symmetric matrix of dimension 100X100 and diagonalizes it. Computed eigenvalues are compared with exact results (from Householder diagonalization).
GNU compilers, e.g.,
module load gcc/13.2.0-fasrc01
gfortran -o lanczos.x lanczos.f90 -O2Intel compilers, e.g.,
module load intel/24.0.1-fasrc01
ifx -o lanczos.x lanczos.f90 -O2#!/usr/bin/env bash
#SBATCH -J lanczos_job
#SBATCH -o lanczos_job.out
#SBATCH -e lanczos_job.err
#SBATCH -N 1
#SBATCH -c 1
#SBATCH -p test
#SBATCH -t 0-00:30
#SBATCH --mem=4G
# Load required software modules
module load gcc/13.2.0-fasrc01
# Run the program
./lanczos.x <<EOF
100
5
100
EOFsbatch run.sbatchcat lanczos_job.out
Enter matrix dimension:
Enter number of eigen-values to compute:
Enter MAX number of iterations ( typically 100 - 300, but <= matrix dim.)
5 lowest eigenvalues - Lanczos, exact
iteration: 1
1 37.445499503187669 50.010946087355670
2 0.0000000000000000 5.1987505309260547
3 0.0000000000000000 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 2
1 49.960983973954548 50.010946087355670
2 0.0000000000000000 5.1987505309260547
3 0.0000000000000000 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 3
1 50.010765095790497 50.010946087355670
2 2.4676249626592508 5.1987505309260547
3 0.0000000000000000 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 4
1 50.010945575435315 50.010946087355670
2 3.8016683537257268 5.1987505309260547
3 0.0000000000000000 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 5
1 50.010946085319084 50.010946087355670
2 4.3032873534543015 5.1987505309260547
3 1.2235573766816881 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 6
1 50.010946087348991 50.010946087355670
2 4.6811829416974327 5.1987505309260547
3 2.6992885673631508 5.1856783411660166
4 0.0000000000000000 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 7
1 50.010946087355677 50.010946087355670
2 4.9137916871547915 5.1987505309260547
3 3.3508828530472030 5.1856783411660166
4 0.64165798116472217 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 8
1 50.010946087355698 50.010946087355670
2 5.0591178779694035 5.1987505309260547
3 3.7666220703099746 5.1856783411660166
4 1.8822611084111309 5.0014143250821714
5 0.0000000000000000 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 9
1 50.010946087355698 50.010946087355670
2 5.1278924439743490 5.1987505309260547
3 4.0046482782297046 5.1856783411660166
4 2.5228428487243244 5.0014143250821714
5 0.29805487878129067 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 10
1 50.010946087355698 50.010946087355670
2 5.1596326365201506 5.1987505309260547
3 4.1674613555015663 5.1856783411660166
4 3.0061840127944186 5.0014143250821714
5 1.4025265082457954 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 11
1 50.010946087355698 50.010946087355670
2 5.1791708343750882 5.1987505309260547
3 4.3376352400377973 5.1856783411660166
4 3.4606618729466252 5.0014143250821714
5 2.1144218670587920 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 12
1 50.010946087355698 50.010946087355670
2 5.1893328488480206 5.1987505309260547
3 4.4680766326723313 5.1856783411660166
4 3.6949668450532376 5.0014143250821714
5 2.4400150899059301 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 13
1 50.010946087355698 50.010946087355670
2 5.1943696773486483 5.1987505309260547
3 4.5567270396572184 5.1856783411660166
4 3.8387613696690330 5.0014143250821714
5 2.7816966964308469 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 14
1 50.010946087355698 50.010946087355670
2 5.1968404255156004 5.1987505309260547
3 4.6168508619602822 5.1856783411660166
4 3.9514420935375796 5.0014143250821714
5 3.1286107051108822 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 15
1 50.010946087355698 50.010946087355670
2 5.1977118594145013 5.1987505309260547
3 4.6468934005063911 5.1856783411660166
4 4.0259267713433760 5.0014143250821714
5 3.3457065702120476 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 16
1 50.010946087355698 50.010946087355670
2 5.1982205784856141 5.1987505309260547
3 4.6750225494860231 5.1856783411660166
4 4.1361969767338875 5.0014143250821714
5 3.6163474942654044 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 17
1 50.010946087355698 50.010946087355670
2 5.1984808823114124 5.1987505309260547
3 4.7006311200627362 5.1856783411660166
4 4.2685156945990954 5.0014143250821714
5 3.7917135682480976 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 18
1 50.010946087355698 50.010946087355670
2 5.1985723815604068 5.1987505309260547
3 4.7157061647807943 5.1856783411660166
4 4.3428722464612708 5.0014143250821714
5 3.8565671476537347 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 19
1 50.010946087355698 50.010946087355670
2 5.1986323076172685 5.1987505309260547
3 4.7337325854416905 5.1856783411660166
4 4.4288891213381518 5.0014143250821714
5 3.9430256110621156 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 20
1 50.010946087355698 50.010946087355670
2 5.1986630794533788 5.1987505309260547
3 4.7529107566552558 5.1856783411660166
4 4.5067590079039528 5.0014143250821714
5 4.0486852278097611 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 21
1 50.010946087355698 50.010946087355670
2 5.1986803425007766 5.1987505309260547
3 4.7746830044325064 5.1856783411660166
4 4.5692505621311819 5.0014143250821714
5 4.1426414983774960 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 22
1 50.010946087355698 50.010946087355670
2 5.1986866325465479 5.1987505309260547
3 4.7885630302741564 5.1856783411660166
4 4.5980407114134945 5.0014143250821714
5 4.1902615918252692 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 23
1 50.010946087355698 50.010946087355670
2 5.1986902181915928 5.1987505309260547
3 4.8016519159069881 5.1856783411660166
4 4.6213712781093053 5.0014143250821714
5 4.2418719526168518 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 24
1 50.010946087355698 50.010946087355670
2 5.1986922098679837 5.1987505309260547
3 4.8144981864787777 5.1856783411660166
4 4.6428859500029311 5.0014143250821714
5 4.3123251735968076 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 25
1 50.010946087355698 50.010946087355670
2 5.1986940694676775 5.1987505309260547
3 4.8406892161717572 5.1856783411660166
4 4.6836279100735334 5.0014143250821714
5 4.4533807922782662 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 26
1 50.010946087355698 50.010946087355670
2 5.1986959001833224 5.1987505309260547
3 4.9016502865679534 5.1856783411660166
4 4.7390166534016771 5.0014143250821714
5 4.5505446868562727 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 27
1 50.010946087355698 50.010946087355670
2 5.1986979403870874 5.1987505309260547
3 4.9849558297703860 5.1856783411660166
4 4.7688465361130410 5.0014143250821714
5 4.5864758122316527 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 28
1 50.010946087355698 50.010946087355670
2 5.1987011053617920 5.1987505309260547
3 5.0668564627869594 5.1856783411660166
4 4.7850999534381948 5.0014143250821714
5 4.6084464817345605 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 29
1 50.010946087355698 50.010946087355670
2 5.1987068989129019 5.1987505309260547
3 5.1272458615601950 5.1856783411660166
4 4.7958350182041736 5.0014143250821714
5 4.6264346776923162 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 30
1 50.010946087355698 50.010946087355670
2 5.1987127856026847 5.1987505309260547
3 5.1512081007648618 5.1856783411660166
4 4.8010010690716687 5.0014143250821714
5 4.6369074408732578 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 31
1 50.010946087355698 50.010946087355670
2 5.1987173710059151 5.1987505309260547
3 5.1614107236199258 5.1856783411660166
4 4.8040816453494379 5.0014143250821714
5 4.6444165706113143 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 32
1 50.010946087355698 50.010946087355670
2 5.1987213552793543 5.1987505309260547
3 5.1674756883346191 5.1856783411660166
4 4.8069944418344024 5.0014143250821714
5 4.6534634533924546 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 33
1 50.010946087355698 50.010946087355670
2 5.1987260342562527 5.1987505309260547
3 5.1726809229234876 5.1856783411660166
4 4.8125775645149718 5.0014143250821714
5 4.6797976159870291 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 34
1 50.010946087355698 50.010946087355670
2 5.1987317465494449 5.1987505309260547
3 5.1772818318719978 5.1856783411660166
4 4.8352604399935011 5.0014143250821714
5 4.7565793071782601 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 35
1 50.010946087355698 50.010946087355670
2 5.1987377691233876 5.1987505309260547
3 5.1807923476067108 5.1856783411660166
4 4.8941977227934030 5.0014143250821714
5 4.7886056664612831 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 36
1 50.010946087355698 50.010946087355670
2 5.1987419092349887 5.1987505309260547
3 5.1826667911814761 5.1856783411660166
4 4.9311318847245689 5.0014143250821714
5 4.7942167987619104 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 37
1 50.010946087355698 50.010946087355670
2 5.1987452784495085 5.1987505309260547
3 5.1839598933086002 5.1856783411660166
4 4.9573760571368730 5.0014143250821714
5 4.7969928672106077 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 38
1 50.010946087355698 50.010946087355670
2 5.1987477110945273 5.1987505309260547
3 5.1847920953368769 5.1856783411660166
4 4.9756743893641247 5.0014143250821714
5 4.7988348164364112 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 39
1 50.010946087355698 50.010946087355670
2 5.1987492412009457 5.1987505309260547
3 5.1852803619475791 5.1856783411660166
4 4.9878501434817606 5.0014143250821714
5 4.8002511130273797 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 40
1 50.010946087355698 50.010946087355670
2 5.1987498804788252 5.1987505309260547
3 5.1854780469452644 5.1856783411660166
4 4.9935425393527515 5.0014143250821714
5 4.8010892277726436 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 41
1 50.010946087355698 50.010946087355670
2 5.1987502672055594 5.1987505309260547
3 5.1855968100060696 5.1856783411660166
4 4.9976419689992246 5.0014143250821714
5 4.8019143909682525 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 42
1 50.010946087355698 50.010946087355670
2 5.1987504568895062 5.1987505309260547
3 5.1856552779477862 5.1856783411660166
4 5.0001522344062144 5.0014143250821714
5 4.8026718738138579 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 43
1 50.010946087355698 50.010946087355670
2 5.1987505129015803 5.1987505309260547
3 5.1856726780845346 5.1856783411660166
4 5.0010553138235982 5.0014143250821714
5 4.8030632167571330 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 44
1 50.010946087355698 50.010946087355670
2 5.1987505264226597 5.1987505309260547
3 5.1856769124757873 5.1856783411660166
4 5.0013089350616422 5.0014143250821714
5 4.8032034398408534 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 45
1 50.010946087355698 50.010946087355670
2 5.1987505293991143 5.1987505309260547
3 5.1856778522177507 5.1856783411660166
4 5.0013728322218380 5.0014143250821714
5 4.8032456969770099 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 46
1 50.010946087355698 50.010946087355670
2 5.1987505303724237 5.1987505309260547
3 5.1856781623184336 5.1856783411660166
4 5.0013970171777125 5.0014143250821714
5 4.8032647854375377 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 47
1 50.010946087355698 50.010946087355670
2 5.1987505308031841 5.1987505309260547
3 5.1856783010807250 5.1856783411660166
4 5.0014098263589535 5.0014143250821714
5 4.8032773918908269 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 48
1 50.010946087355698 50.010946087355670
2 5.1987505309021653 5.1987505309260547
3 5.1856783333087977 5.1856783411660166
4 5.0014133315028149 5.0014143250821714
5 4.8032816811180901 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 49
1 50.010946087355698 50.010946087355670
2 5.1987505309214930 5.1987505309260547
3 5.1856783396530295 5.1856783411660166
4 5.0014141100739851 5.0014143250821714
5 4.8032827942040557 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 50
1 50.010946087355698 50.010946087355670
2 5.1987505309249702 5.1987505309260547
3 5.1856783408003757 5.1856783411660166
4 5.0014142665273793 5.0014143250821714
5 4.8032830484498348 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 51
1 50.010946087355698 50.010946087355670
2 5.1987505309258006 5.1987505309260547
3 5.1856783410770246 5.1856783411660166
4 5.0014143088782230 5.0014143250821714
5 4.8032831274422989 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 52
1 50.010946087355698 50.010946087355670
2 5.1987505309260031 5.1987505309260547
3 5.1856783411458247 5.1856783411660166
4 5.0014143209168900 5.0014143250821714
5 4.8032831538228651 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 53
1 50.010946087355698 50.010946087355670
2 5.1987505309260493 5.1987505309260547
3 5.1856783411625047 5.1856783411660166
4 5.0014143242675866 5.0014143250821714
5 4.8032831625100387 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 54
1 50.010946087355698 50.010946087355670
2 5.1987505309260582 5.1987505309260547
3 5.1856783411655458 5.1856783411660166
4 5.0014143249584402 5.0014143250821714
5 4.8032831645915142 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 55
1 50.010946087355698 50.010946087355670
2 5.1987505309260627 5.1987505309260547
3 5.1856783411659118 5.1856783411660166
4 5.0014143250500522 5.0014143250821714
5 4.8032831649063228 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 56
1 50.010946087355698 50.010946087355670
2 5.1987505309260600 5.1987505309260547
3 5.1856783411660015 5.1856783411660166
4 5.0014143250750953 5.0014143250821714
5 4.8032831650043581 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 57
1 50.010946087355698 50.010946087355670
2 5.1987505309260564 5.1987505309260547
3 5.1856783411660157 5.1856783411660166
4 5.0014143250805247 5.0014143250821714
5 4.8032831650285646 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 58
1 50.010946087355698 50.010946087355670
2 5.1987505309260573 5.1987505309260547
3 5.1856783411660263 5.1856783411660166
4 5.0014143250819334 5.0014143250821714
5 4.8032831650357259 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 59
1 50.010946087355698 50.010946087355670
2 5.1987505309260600 5.1987505309260547
3 5.1856783411660148 5.1856783411660166
4 5.0014143250821297 5.0014143250821714
5 4.8032831650368779 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 60
1 50.010946087355698 50.010946087355670
2 5.1987505309260627 5.1987505309260547
3 5.1856783411660139 5.1856783411660166
4 5.0014143250821741 5.0014143250821714
5 4.8032831650371648 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 61
1 50.010946087355698 50.010946087355670
2 5.1987505309260635 5.1987505309260547
3 5.1856783411660219 5.1856783411660166
4 5.0014143250821803 5.0014143250821714
5 4.8032831650371959 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 62
1 50.010946087355698 50.010946087355670
2 5.1987505309260618 5.1987505309260547
3 5.1856783411660228 5.1856783411660166
4 5.0014143250821768 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 63
1 50.010946087355698 50.010946087355670
2 5.1987505309260582 5.1987505309260547
3 5.1856783411660219 5.1856783411660166
4 5.0014143250821794 5.0014143250821714
5 4.8032831650372065 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 64
1 50.010946087355698 50.010946087355670
2 5.1987505309260671 5.1987505309260547
3 5.1856783411660299 5.1856783411660166
4 5.0014143250821821 5.0014143250821714
5 4.8032831650372101 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 65
1 50.010946087355698 50.010946087355670
2 5.1987505309260609 5.1987505309260547
3 5.1856783411660174 5.1856783411660166
4 5.0014143250821723 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 66
1 50.010946087355698 50.010946087355670
2 5.1987505309260644 5.1987505309260547
3 5.1856783411660174 5.1856783411660166
4 5.0014143250821759 5.0014143250821714
5 4.8032831650372074 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 67
1 50.010946087355698 50.010946087355670
2 5.1987505309260627 5.1987505309260547
3 5.1856783411660183 5.1856783411660166
4 5.0014143250821839 5.0014143250821714
5 4.8032831650372048 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 68
1 50.010946087355698 50.010946087355670
2 5.1987505309260600 5.1987505309260547
3 5.1856783411660237 5.1856783411660166
4 5.0014143250821768 5.0014143250821714
5 4.8032831650372065 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 69
1 50.010946087355698 50.010946087355670
2 5.1987505309260609 5.1987505309260547
3 5.1856783411660192 5.1856783411660166
4 5.0014143250821865 5.0014143250821714
5 4.8032831650371985 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 70
1 50.010946087355698 50.010946087355670
2 5.1987505309260635 5.1987505309260547
3 5.1856783411660210 5.1856783411660166
4 5.0014143250821768 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 71
1 50.010946087355698 50.010946087355670
2 5.1987505309260627 5.1987505309260547
3 5.1856783411660183 5.1856783411660166
4 5.0014143250821865 5.0014143250821714
5 4.8032831650372074 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 72
1 50.010946087355698 50.010946087355670
2 5.1987505309260591 5.1987505309260547
3 5.1856783411660130 5.1856783411660166
4 5.0014143250821839 5.0014143250821714
5 4.8032831650372012 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 73
1 50.010946087355698 50.010946087355670
2 5.1987505309260635 5.1987505309260547
3 5.1856783411660112 5.1856783411660166
4 5.0014143250821803 5.0014143250821714
5 4.8032831650372048 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 74
1 50.010946087355698 50.010946087355670
2 5.1987505309260627 5.1987505309260547
3 5.1856783411660237 5.1856783411660166
4 5.0014143250821776 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 75
1 50.010946087355698 50.010946087355670
2 5.1987505309260671 5.1987505309260547
3 5.1856783411660237 5.1856783411660166
4 5.0014143250821759 5.0014143250821714
5 4.8032831650372119 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 76
1 50.010946087355698 50.010946087355670
2 5.1987505309260538 5.1987505309260547
3 5.1856783411660201 5.1856783411660166
4 5.0014143250821865 5.0014143250821714
5 4.8032831650372039 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 77
1 50.010946087355698 50.010946087355670
2 5.1987505309260609 5.1987505309260547
3 5.1856783411660148 5.1856783411660166
4 5.0014143250821750 5.0014143250821714
5 4.8032831650372021 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 78
1 50.010946087355698 50.010946087355670
2 5.1987505309260591 5.1987505309260547
3 5.1856783411660228 5.1856783411660166
4 5.0014143250821865 5.0014143250821714
5 4.8032831650372101 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 79
1 50.010946087355698 50.010946087355670
2 5.1987505309260618 5.1987505309260547
3 5.1856783411660272 5.1856783411660166
4 5.0014143250821830 5.0014143250821714
5 4.8032831650372074 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 80
1 50.010946087355698 50.010946087355670
2 5.1987505309260715 5.1987505309260547
3 5.1856783411660210 5.1856783411660166
4 5.0014143250821794 5.0014143250821714
5 4.8032831650372101 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 81
1 50.010946087355698 50.010946087355670
2 5.1987505309260715 5.1987505309260547
3 5.1856783411660166 5.1856783411660166
4 5.0014143250821723 5.0014143250821714
5 4.8032831650372119 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 82
1 50.010946087355698 50.010946087355670
2 5.1987505309260618 5.1987505309260547
3 5.1856783411660210 5.1856783411660166
4 5.0014143250821785 5.0014143250821714
5 4.8032831650372074 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 83
1 50.010946087355698 50.010946087355670
2 5.1987505309260662 5.1987505309260547
3 5.1856783411660299 5.1856783411660166
4 5.0014143250821803 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 84
1 50.010946087355698 50.010946087355670
2 5.1987505309260609 5.1987505309260547
3 5.1856783411660343 5.1856783411660166
4 5.0014143250821901 5.0014143250821714
5 4.8032831650372119 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 85
1 50.010946087355698 50.010946087355670
2 5.1987505309260600 5.1987505309260547
3 5.1856783411660183 5.1856783411660166
4 5.0014143250821856 5.0014143250821714
5 4.8032831650372092 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 86
1 50.010946087355698 50.010946087355670
2 5.1987505309260680 5.1987505309260547
3 5.1856783411660077 5.1856783411660166
4 5.0014143250821812 5.0014143250821714
5 4.8032831650372092 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 87
1 50.010946087355698 50.010946087355670
2 5.1987505309260564 5.1987505309260547
3 5.1856783411660183 5.1856783411660166
4 5.0014143250821839 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 88
1 50.010946087355698 50.010946087355670
2 5.1987505309260635 5.1987505309260547
3 5.1856783411660103 5.1856783411660166
4 5.0014143250821919 5.0014143250821714
5 4.8032831650372181 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 89
1 50.010946087355698 50.010946087355670
2 5.1987505309260618 5.1987505309260547
3 5.1856783411660130 5.1856783411660166
4 5.0014143250821750 5.0014143250821714
5 4.8032831650371994 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 90
1 50.010946087355698 50.010946087355670
2 5.1987505309260538 5.1987505309260547
3 5.1856783411660210 5.1856783411660166
4 5.0014143250821714 5.0014143250821714
5 4.8032831650372128 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 91
1 50.010946087355698 50.010946087355670
2 5.1987505309260653 5.1987505309260547
3 5.1856783411660290 5.1856783411660166
4 5.0014143250821732 5.0014143250821714
5 4.8032831650371923 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 92
1 50.010946087355698 50.010946087355670
2 5.1987505309260671 5.1987505309260547
3 5.1856783411660246 5.1856783411660166
4 5.0014143250821883 5.0014143250821714
5 4.8032831650371994 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 93
1 50.010946087355698 50.010946087355670
2 5.1987505309260600 5.1987505309260547
3 5.1856783411660112 5.1856783411660166
4 5.0014143250821759 5.0014143250821714
5 4.8032831650372119 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 94
1 50.010946087355698 50.010946087355670
2 5.1987505309260396 5.1987505309260547
3 5.1856783411660210 5.1856783411660166
4 5.0014143250822114 5.0014143250821714
5 4.8032831650372234 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 95
1 50.010946087355698 50.010946087355670
2 5.1987505309260662 5.1987505309260547
3 5.1856783411660139 5.1856783411660166
4 5.0014143250821892 5.0014143250821714
5 4.8032831650371985 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 96
1 50.010946087355698 50.010946087355670
2 5.1987505309260573 5.1987505309260547
3 5.1856783411660237 5.1856783411660166
4 5.0014143250821572 5.0014143250821714
5 4.8032831650372056 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 97
1 50.010946087355698 50.010946087355670
2 5.1987505309260618 5.1987505309260547
3 5.1856783411660157 5.1856783411660166
4 5.0014143250821830 5.0014143250821714
5 4.8032831650371968 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 98
1 50.010946087355698 50.010946087355670
2 5.1987505309260742 5.1987505309260547
3 5.1856783411660121 5.1856783411660166
4 5.0014143250821652 5.0014143250821714
5 4.8032831650371950 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 99
1 50.010946087355698 50.010946087355670
2 5.1987505309260875 5.1987505309260547
3 5.1856783411660352 5.1856783411660166
4 5.0014143250821634 5.0014143250821714
5 4.8032831650372074 4.8032831650372225
5 lowest eigenvalues - Lanczos, exact
iteration: 100
1 50.010946087355698 50.010946087355670
2 5.1987505309260538 5.1987505309260547
3 5.1856783411659926 5.1856783411660166
4 5.0014143250821697 5.0014143250821714
5 4.8032831650372074 4.8032831650372225