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-324.98400 (size) -326.01900 (is) -326.01100 (relati) 24.98600 (v) 14.98280 (ely) -326.01700 (small) -325.01600 (compared) -326.01400 (to) -326.01200 (the) -326.01700 (frame) ] TJ T* [ (size) -227.01700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 71.18320 128.00300 Tm (6) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 76.16450 128.00300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 80.91680 128.00300 Tm (21) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 90.87930 128.00300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 95.64140 128.00300 Tm (34) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 105.60400 128.00300 Tm [ (\135\056) -226.98300 (Therefore\054) -232.00700 (one) -227.01500 (can) -226.98500 (naturally) -226.99600 (consider) -227.00400 (a) -228.00600 (ma\055) ] TJ -55.49180 -11.95510 Td [ (trix) -296.01300 (decomposition) -296.98700 (problem) -296.00200 (by) -296.01900 (writing) ] TJ /R34 9.96260 Tf 159.22000 0 Td (A) Tj /R28 9.96260 Tf 10.42500 0 Td [ (as) -295.98700 (the) -297.00200 (sum) -296.00700 (of) -297.00700 (its) ] TJ -169.64500 -11.95510 Td [ (background) -250.01300 (and) -249.99100 (fore) 15.01100 (ground\072) ] TJ /R34 9.96260 Tf 92.90510 -19.50660 Td (A) Tj /R44 9.96260 Tf 10.23980 0 Td [ (\075) -0.80011 ] TJ /R34 9.96260 Tf 10.51600 0 Td [ (B) -0.49992 ] TJ /R44 9.96260 Tf 10.26990 0 Td [ (\053) -0.80011 ] TJ /R34 9.96260 Tf 9.96289 0 Td [ (F) -28.10320 (\073) -0.80011 ] TJ /R28 9.96260 Tf 124.85600 468.19300 Td (where) Tj /R34 9.96260 Tf 28.59380 0 Td [ (B) -50.49160 (\073) -167.78800 (F) -0.10047 ] TJ /R40 9.96260 Tf 26.31130 0 Td [ (2) -0.70086 ] TJ /R42 9.96260 Tf 12.67770 0 Td [ (R) -0.20095 ] TJ /R38 6.97380 Tf 7.19492 3.61602 Td [ (m) -0.70017 ] TJ /R48 6.97380 Tf 7.07031 0 Td [ <02> -0.89971 ] TJ /R38 6.97380 Tf 6.22578 0 Td [ (n) -0.19955 ] TJ /R28 9.96260 Tf 9.67891 -3.61602 Td [ (are) -426.99700 (the) -427.01700 (lo) 24.98600 (w\055rank) -428.00700 (background) -427.00200 (and) ] TJ -97.75270 -11.95510 Td [ (sparse) -271.00900 (fore) 15.01220 (ground) -272.01100 (matrices\054) -276.99300 (respecti) 24.98600 (v) 14.98280 (ely) 65.01860 (\056) -271.00900 (Therefore\054) -277.01700 (RPCA) ] TJ 11.95510 TL T* [ (solv) 15 (es\072) ] TJ /R44 9.96260 Tf 65.45080 -8.35508 Td [ (m) -0.29897 (i) -0.79889 (n) -0.60039 ] TJ /R38 6.97380 Tf 5.12305 -6.42578 Td [ (B) -0.19955 ] TJ /R40 9.96260 Tf 13.14220 6.42578 Td (k) Tj /R34 9.96260 Tf 4.98086 0 Td (A) Tj /R40 9.96260 Tf 9.68594 0 Td [ <00> -0.80379 ] TJ /R34 9.96260 Tf 9.96328 0 Td [ (B) -0.49992 ] TJ /R40 9.96260 Tf 8.05586 0 Td (k) Tj /R38 6.97380 Tf 4.98203 -1.49375 Td [ (\140) -0.19605 ] TJ /R50 4.98130 Tf 3.33398 -0.99727 Td [ (1) -0.59794 ] TJ /R44 9.96260 Tf 6.60117 2.49102 Td [ (\053) -0.80379 ] TJ /R34 9.96260 Tf 9.96172 0 Td [ <15> -0.29897 ] TJ /R40 9.96260 Tf 5.81211 0 Td (k) Tj /R34 9.96260 Tf 4.98086 0 Td [ (B) -0.49992 ] TJ /R40 9.96260 Tf 8.05703 0 Td (k) Tj /R48 6.97380 Tf 4.98125 -1.49375 Td [ <03> -0.30107 ] TJ /R34 9.96260 Tf 4.57969 1.49375 Td [ (\073) -0.80379 ] TJ /R28 9.96260 Tf 54.94220 0 Td (\0501\051) Tj -224.63400 -20.64800 Td (where) Tj /R40 9.96260 Tf 26.96290 0 Td [ (k) -231.99600 <01> -232.79700 (k) ] TJ /R38 6.97380 Tf 17.35590 -1.49492 Td [ (\140) -0.19955 ] TJ /R50 4.98130 Tf 3.33516 -0.99609 Td [ (1) -0.60284 ] TJ /R28 9.96260 Tf 7.01094 2.49102 Td (and) Tj /R40 9.96260 Tf 17.01090 0 Td [ (k) -231.99600 <01> -232.79700 (k) ] TJ /R48 6.97380 Tf 17.35620 -1.49492 Td [ <03> -0.30107 ] TJ /R28 9.96260 Tf 7.20469 1.49492 Td [ (denote) -263 (the) ] TJ /R34 9.96260 Tf 43.98320 0 Td [ (\140) -0.70086 ] TJ /R46 6.97380 Tf 4.15078 -1.49492 Td [ (1) -0.49712 ] TJ /R28 9.96260 Tf 7.09414 1.49492 Td [ (norm) -262.99500 (and) -263.99000 (the) -263.00500 (nuclear) ] TJ -151.46500 -11.95470 Td [ (norm) -252.01700 (\050sum) -252.01700 (of) -251.01400 (the) -251.99000 (singular) -252.00700 (v) 24.98110 (alues\051) -251.99200 (of) -251.99700 (mat) 0.99493 (rices\054) -253.01200 (respecti) 24.98600 (v) 14.98280 (ely) 65.01860 (\054) ] TJ 11.95630 TL (and) ' /R34 9.96260 Tf 16.87700 0 Td [ <15> -278.30600 (\076) -0.79889 ] TJ /R44 9.96260 Tf 19.09490 0 Td (0) Tj /R28 9.96260 Tf 7.47187 0 Td [ (is) -249.98500 (a) -250.00200 (balancing) -250.01500 (parameter) 55.01040 (\056) ] TJ -31.48910 -11.95470 Td [ (In) -660.00500 (contrast\054) -762.98800 (consider) -661.01200 (a) -660.01200 (situation) -660.98300 (when) -659.99800 (a) -660.01200 (fe) 25.00560 (w) 65.01370 (\054) -660.98300 (say) ] TJ /R34 9.96260 Tf -11.95470 -11.95510 Td [ (k) -0.60039 ] TJ /R28 9.96260 Tf 5.50000 0 Td [ (\054) -777.00500 (principal) -671 (directions) -672.01300 (are) -670.99600 (already) -672.00500 <7370656369026564> -671 (and) -672 (one) ] TJ -5.50000 -11.95510 Td [ (w) 10 (ants) -407.01500 (to) -407.01800 <026e64> -407.00600 (a) -406.99600 (rank) ] TJ /R34 9.96260 Tf 88.79880 0 Td [ (r) -0.19850 ] TJ /R28 9.96260 Tf 8.82695 0 Td [ (approximation) -407.01500 (of) -406.99100 (the) -406.98100 (data\054) -446 (where) ] TJ /R34 9.96260 Tf -97.62580 -11.95510 Td [ (k) -0.60039 ] TJ /R40 9.96260 Tf 12.24880 0 Td [ <14> -0.79889 ] TJ /R34 9.96260 Tf 14.49690 0 Td [ (r) -0.19850 ] TJ /R28 9.96260 Tf 4.77227 0 Td [ (\056) -465.99800 (In) -465.99800 (1987\054) -518.98900 (Golub) ] TJ /R32 9.96260 Tf 77.21210 0 Td [ (et) -465.99600 (al) ] TJ /R28 9.96260 Tf 19.59380 0 Td [ (\056) -465.99600 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 447.63700 428.13500 Tm (13) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R28 9.96260 Tf 1 0 0 1 457.59900 428.13500 Tm [ (\135) -466.00600 (formulated) -464.99600 (the) -465.99100 (fol\055) ] TJ -148.73700 -11.95590 Td [ (lo) 24.98850 (wing) -498.01500 (constrained) -496.99100 (lo) 24.98850 (w\055rank) -497.99500 (approximation) -497.98100 (problem) -498.01000 (\050to) ] TJ 11.95510 TL T* [ (be) -434.98600 (referred) -435.98900 (as) -434.98400 (GHS) -435.98600 (from) -435.01600 (no) 24.98600 (w) -436 (on\051) -435.02100 (to) -435.99600 (address) -435.01600 (this) -436.02000 (situa\055) ] TJ T* [ (tion\072) -287.99900 (Gi) 24.98600 (v) 14.98280 (en) ] TJ /R34 9.96260 Tf 47.95080 0 Td (A) Tj /R44 9.96260 Tf 10.93200 0 Td [ (\075) -347.79200 (\050) -0.90181 ] TJ /R34 9.96260 Tf 15.08320 0 Td (A) Tj /R46 6.97380 Tf 7.47187 -1.49375 Td [ (1) -0.50062 ] TJ /R34 9.96260 Tf 7.93008 1.49375 Td (A) Tj /R46 6.97380 Tf 7.47187 -1.49375 Td [ (2) -0.49712 ] TJ /R44 9.96260 Tf 4.46914 1.49375 Td [ (\051) -0.90181 ] TJ /R40 9.96260 Tf 7.33398 0 Td [ (2) -0.69596 ] TJ /R42 9.96260 Tf 10.10200 0 Td [ (R) -0.19605 ] TJ /R38 6.97380 Tf 7.19492 3.61523 Td [ (m) -0.70017 ] TJ /R48 6.97380 Tf 7.06992 0 Td [ <02> -0.90321 ] TJ /R38 6.97380 Tf 6.22695 0 Td [ (n) -0.20305 ] TJ /R28 9.96260 Tf 8.28711 -3.61523 Td (with) Tj /R34 9.96260 Tf 20.57890 0 Td (A) Tj /R46 6.97380 Tf 7.47227 -1.49375 Td [ (1) -0.49712 ] TJ /R40 9.96260 Tf 7.92891 1.49375 Td [ (2) -0.69596 ] TJ /R42 9.96260 Tf 10.10200 0 Td [ (R) -0.19605 ] TJ /R38 6.97380 Tf 7.19492 3.61523 Td [ (m) -0.70017 ] TJ /R48 6.97380 Tf 7.06992 0 Td [ <02> -0.90321 ] TJ /R38 6.97380 Tf 6.22617 0 Td [ (k) -0.30107 ] TJ /R28 9.96260 Tf 7.76719 -3.61523 Td (and) Tj /R34 9.96260 Tf -221.86400 -11.95470 Td (A) Tj /R46 6.97380 Tf 7.47187 -1.49414 Td [ (2) -0.50062 ] TJ /R40 9.96260 Tf 7.23711 1.49414 Td [ (2) -0.70086 ] TJ /R42 9.96260 Tf 9.40898 0 Td [ (R) -0.20095 ] TJ /R38 6.97380 Tf 7.19492 3.61484 Td [ (m) -0.70017 ] TJ /R48 6.97380 Tf 7.06992 0 Td [ <02> -0.89971 ] TJ /R46 6.97380 Tf 6.22617 0 Td [ (\050) -0.40259 ] TJ /R38 6.97380 Tf 3.11406 0 Td [ (n) -0.19955 ] TJ /R48 6.97380 Tf 4.92500 0 Td [ <00> -0.89971 ] TJ /R38 6.97380 Tf 6.22578 0 Td [ (k) -0.29757 ] TJ /R46 6.97380 Tf 4.40391 0 Td [ (\051) -0.40259 ] TJ /R28 9.96260 Tf 3.61094 -3.61484 Td [ (\054) -249.99500 <026e64> ] TJ /R34 9.96260 Tf 22.97420 0 Td (A) Tj /R38 6.97380 Tf 7.47187 -1.49414 Td [ (G) -0.39909 ] TJ /R44 9.96260 Tf 9.46797 1.49414 Td [ (\075) -278.78700 (\050) -0.90181 ] TJ 16.75900 2.51797 Td (\176) Tj /R34 9.96260 Tf -2.36797 -2.51797 Td [ (B) -0.49992 ] TJ /R46 6.97380 Tf 7.55625 -1.49414 Td [ (1) -0.49712 ] TJ /R44 9.96260 Tf 9.60469 4.01211 Td (\176) Tj /R34 9.96260 Tf -2.36797 -2.51797 Td [ (B) -0.49992 ] TJ /R46 6.97380 Tf 7.55703 -1.49414 Td [ (2) -0.49712 ] TJ /R44 9.96260 Tf 4.46914 1.49414 Td [ (\051) -0.90181 ] TJ /R28 9.96260 Tf 6.36484 0 Td [ (such) -249.98800 (that) ] TJ /R44 9.96260 Tf -122.72500 -18.47300 Td [ (\050) -0.90181 ] TJ 6.24219 2.51797 Td (\176) Tj /R34 9.96260 Tf -2.36797 -2.51797 Td [ (B) -0.49992 ] TJ /R46 6.97380 Tf 7.55703 -1.49492 Td [ (1) -0.50062 ] TJ /R44 9.96260 Tf 9.60391 4.01289 Td (\176) Tj /R34 9.96260 Tf -2.36719 -2.51797 Td [ (B) -0.49992 ] TJ /R46 6.97380 Tf 7.55625 -1.49492 Td [ (2) -0.50062 ] TJ /R44 9.96260 Tf 4.46992 1.49492 Td [ (\051) -278.90900 (\075) -277.80400 (ar) -0.69841 (g) -1395.01000 (m) -0.30387 (i) -0.79889 (n) -0.60284 ] TJ /R38 6.97380 Tf 32.82110 -6.89102 Td [ (B) -0.19605 ] TJ /R46 6.97380 Tf 6.35898 0 Td [ (\075\050) -0.40610 ] TJ /R38 6.97380 Tf 9.22891 0 Td [ (B) -0.19605 ] TJ /R50 4.98130 Tf 6.01992 -0.99609 Td [ (1) -0.59794 ] TJ /R38 6.97380 Tf 6.15586 0.99609 Td [ (B) -0.19605 ] TJ /R50 4.98130 Tf 6.02031 -0.99609 Td [ (2) -0.59794 ] TJ /R46 6.97380 Tf 3.88789 0.99609 Td [ (\051) -0.39909 ] TJ /R38 6.97380 Tf -30.23090 -7.52500 Td [ (B) -0.19605 ] TJ /R50 4.98130 Tf 6.01875 -0.99609 Td [ (1) -0.59794 ] TJ /R46 6.97380 Tf 3.88906 0.99609 Td (\075) Tj /R38 6.97380 Tf 6.11602 0 Td [ (A) -0.10502 ] TJ /R50 4.98130 Tf 5.99102 -0.99609 Td [ (1) -0.59794 ] TJ /R46 6.97380 Tf -28.26210 -6.24688 Td [ (r) -0.40259 (a) -0.49712 (n) -1.00124 (k) -0.20305 (\050) -0.39909 ] TJ /R38 6.97380 Tf 18.78400 0 Td [ (B) -0.19605 ] TJ /R46 6.97380 Tf 6.35898 0 Td [ (\051) -0.39909 ] TJ /R48 6.97380 Tf 3.11406 0 Td [ <14> -0.90321 ] TJ /R38 6.97380 Tf 6.22617 0 Td [ (r) -0.40610 ] TJ /R40 9.96260 Tf 6.76914 21.65900 Td (k) Tj /R34 9.96260 Tf 4.98086 0 Td (A) Tj /R40 9.96260 Tf 9.68594 0 Td [ <00> -0.80379 ] TJ /R34 9.96260 Tf 9.96211 0 Td [ (B) -0.49992 ] TJ /R40 9.96260 Tf 8.05703 0 Td (k) Tj /R46 6.97380 Tf 4.98086 4.11289 Td [ (2) -0.49712 ] TJ /R38 6.97380 Tf 6.57617 TL T* [ (F) -0.50412 ] TJ /R34 9.96260 Tf 6.62422 2.46328 Td [ (\073) -0.80379 ] TJ /R28 9.96260 Tf 42.72890 0 Td (\0502\051) Tj -224.63400 -37.67300 Td (where) Tj /R40 9.96260 Tf 27.03090 0 Td [ (k) -237.01400 <01> -237.81600 (k) ] TJ /R38 6.97380 Tf 17.45590 -1.49414 Td [ (F) -0.50062 ] TJ /R28 9.96260 Tf 9.31523 1.49414 Td [ (denotes) -270.01400 (the) -269.98700 (Frobenius) -271.01400 (norm) -270.01400 (of) -269.99400 (matrices\056) -270.01400 (That) ] TJ -53.80200 -11.95510 Td [ (is\054) -566.00800 (Golub) ] TJ /R32 9.96260 Tf 44.68280 0 Td [ (et) -501.99200 (al) ] TJ /R28 9.96260 Tf 19.95900 0 Td [ (\056) -501.99200 (required) -503.00900 (a) -502 (fe) 25.00560 (w) -503.00900 (columns\054) ] TJ /R34 9.96260 Tf 116.70600 0 Td (A) Tj /R46 6.97380 Tf 7.47187 -1.49492 Td [ (1) -0.49712 ] TJ /R34 9.96260 Tf 4.46875 1.49492 Td [ (\073) -0.80379 ] TJ /R28 9.96260 Tf 7.77422 0 Td (of) Tj /R34 9.96260 Tf 13.30390 0 Td (A) Tj /R28 9.96260 Tf 12.47810 0 Td (be) Tj -226.84500 -11.95510 Td [ (preserv) 15.01710 (ed) -394.01300 (to) -392.98100 <026e64> -393.98800 (a) -394.01800 (lo) 24.98850 (w) -392.99100 (rank) -394.01300 (approximation) -392.97900 (of) ] TJ /R44 9.96260 Tf 196.43400 0 Td [ (\050) -0.90181 ] TJ /R34 9.96260 Tf 3.87383 0 Td (A) Tj /R46 6.97380 Tf 7.47227 -1.49492 Td [ (1) -0.49712 ] TJ /R34 9.96260 Tf 9.88672 1.49492 Td (A) Tj /R46 6.97380 Tf 7.47227 -1.49492 Td [ (2) -0.49712 ] TJ /R44 9.96260 Tf 4.46875 1.49492 Td [ (\051) -0.90181 ] TJ /R34 9.96260 Tf 3.87500 0 Td [ (\072) -0.80379 ] TJ /R28 9.96260 Tf -233.48300 -11.95590 Td (When) Tj /R34 9.96260 Tf 27.79180 0 Td (A) Tj /R46 6.97380 Tf 7.47227 -1.49414 Td [ (1) -0.50062 ] TJ /R44 9.96260 Tf 10.03480 1.49414 Td [ (\075) -0.79889 ] TJ /R40 9.96260 Tf 13.31520 0 Td (\073) Tj /R28 9.96260 Tf 4.98086 0 Td [ (\054) -440.00300 (we) -400.99400 (are) -401.98400 (back) -402.01100 (to) -401.02100 (the) -402.00200 (standard) -401.99700 (problem) -401.00700 (of) ] TJ -63.59490 -11.95510 Td [ (lo) 24.98850 (w\055rank) -249.99500 (approximation\072) -310.00700 <026e64> ] TJ /R44 9.96260 Tf 122.53600 2.51914 Td (\176) Tj /R34 9.96260 Tf -2.36797 -2.51914 Td [ (B) -0.49992 ] TJ /R28 9.96260 Tf 10.54800 0 Td [ (such) -249.98800 (that) ] TJ /R44 9.96260 Tf -82.24530 -15.95510 Td (\176) Tj /R34 9.96260 Tf -2.36797 -2.51797 Td [ (B) -0.49992 ] TJ /R44 9.96260 Tf 10.82420 0 Td [ (\075) -278.78400 (ar) -0.69841 (g) -1274.01000 (m) -0.30387 (i) -0.79889 (n) -0.60284 ] TJ /R38 6.97380 Tf 42.19800 -6.42578 Td [ (B) -0.19605 ] TJ /R46 6.97380 Tf -16.01910 -6.24688 Td [ (r) -0.40259 (a) -0.50062 (n) -0.99774 (k) -0.19955 (\050) -0.39909 ] TJ /R38 6.97380 Tf 18.78400 0 Td [ (B) -0.19605 ] TJ /R46 6.97380 Tf 6.35898 0 Td [ (\051) -0.39909 ] TJ /R48 6.97380 Tf 3.11406 0 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