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[ 1 0 2]
[ 0 1 -1]
[-1 1 1]
[2.00000000000000, 2.00000000000000, 1.00000000000000]
The spectral radius of A is 2.
[1/4 0]
[1/4 1/4]
[ 1/8 0]
[3/16 1/8]
[
[1 0] [1/2 0] [1/4 0] [ 1/8 0] [1/16 0] [1/32 0]
[0 1], [1/4 1/2], [1/4 1/4], [3/16 1/8], [ 1/8 1/16], [5/64 1/32],
[1/64 0] [1/128 0] [1/256 0] [ 1/512 0]
[3/64 1/64], [7/256 1/128], [ 1/64 1/256], [9/1024 1/512]
]
[9.33263618503219e-302 0.000000000000000]
[4.66631809251609e-299 9.33263618503219e-302]
[1/2, 1/2]
We say that is convergent.
Example
T (Jacobi): [0.368403149864, 0.368403149864, 0.368403149864]
T (Gauss-Seidel): [0.0, 0.166666666667, 0.1]
T (SOR (omega=1.25): [0.68800410828, 0.150700431987, 0.150700431987]
(1.33333333333333, 0.250000000000000, 0.200000000000000) 1.33333333333333
(1.31666666666667, -0.466666666666667, 0.366666666666667) 0.716666666666667
(1.61111111111111, -0.500000000000000, 0.650000000000000) 0.294444444444444
(1.71666666666667, -0.718055555555556, 0.722222222222222) 0.218055555555556
(1.81342592592593, -0.788888888888889, 0.830555555555556) 0.108333333333333
(1.87314814814815, -0.864351851851852, 0.878240740740741) 0.0754629629629630
(1.91419753086420, -0.906134259259259, 0.920370370370370) 0.0421296296296296
(1.94216820987654, -0.937191358024691, 0.945293209876543) 0.0310570987654321
(1.96082818930041, -0.957407407407407, 0.963310185185185) 0.0202160493827160
(1.97357253086420, -0.971241640946502, 0.975128600823045) 0.0138342335390947
(1.33333333333333, -0.416666666666667, 0.633333333333333) 1.33333333333333
(1.68333333333333, -0.750000000000000, 0.836666666666667) 0.350000000000000
(1.86222222222222, -0.890277777777778, 0.928555555555556) 0.178888888888889
(1.93961111111111, -0.951944444444444, 0.968700000000000) 0.0773888888888889
(1.97354814814815, -0.978949074074074, 0.986289259259259) 0.0339370370370370
(1.98841277777778, -0.990778703703704, 0.993994037037037) 0.0148646296296296
(1.99492424691358, -0.995960632716049, 0.997369102469136) 0.00651146913580247
(1.99777657839506, -0.998230564814815, 0.998847541604938) 0.00285233148148148
(1.99902603547325, -0.999224903137860, 0.999495168349794) 0.00124945707818930
(1.99957335716255, -0.999660470668724, 0.999778859700000) 0.000547321689300411
(1.66666666666667, -0.729166666666667, 1.03125000000000) 1.66666666666667
(1.98350694444444, -1.06716579861111, 1.02164713541667) 0.337999131944444
(2.04112865306713, -1.01567868833189, 1.01270972357856) 0.0576217086226852
(2.00154634169590, -1.00101858009527, 0.997718444576970) 0.0395823113712268
(1.99908717485612, -0.998461853191563, 0.999573109165570) 0.00255672690370432
(1.99940944060144, -0.999882033692251, 0.999900099705093) 0.00142018050068742
(2.00005686209853, -1.00003381154636, 1.00005609637154) 0.000647421497091728
(2.00002324610783, -1.00002360604691, 1.00000359045753) 0.0000525059140156560
(2.00000552034989, -0.999998670724931, 0.999999817835557) 0.0000249353219759930
(1.99999799014606, -0.999999019233669, 0.999999052694461) 7.53020382627932e-6