CONTOH METODE ITERASI JACOBI

1 TENTUKAN SOLUSI SPL4x - y + z = 7

4x - 8y +z = -21(- 2x) + y + 5z = 15

solusi sejatinya adalah (2, 4, 3)penyelesaian:

x r+1 = (7+ yr - zr)/4yr+1 = (21 + 4xr + yr)/8zr+1 = (15 + 2xr - yr)/5

iterasi x y z Ԑx (%) Ԑy (%) Ԑz (%)0 1.000000 2.000000 2.000000 0.000000 0.000000 0.0000001 1.750000 3.375000 3.000000 42.857143 40.740741 33.3333332 1.843750 3.875000 3.025000 5.084746 12.903226 0.8264463 1.962500 3.925000 2.962500 6.050955 1.273885 2.1097054 1.990625 3.976563 3.000000 1.412873 1.296660 1.2500005 1.994141 3.995313 3.000938 0.176298 0.469300 0.0312406 1.998594 3.997188 2.998594 0.222813 0.046908 0.0781627 1.999648 3.999121 3.000000 0.052744 0.048350 0.0468758 1.999780 3.999824 3.000035 0.006593 0.017579 0.0011729 1.999947 3.999895 2.999947 0.008350 0.001758 0.002930

10 1.999987 3.999967 3.000000 0.001978 0.001813 0.00175811 1.999992 3.999993 3.000001 0.000247 0.000659 0.00004412 1.999998 3.999996 2.999998 0.000313 0.000066 0.00011013 2.000000 3.999999 3.000000 0.000074 0.000068 0.00006614 2.000000 4.000000 3.000000 0.000009 0.000025 0.00000215 2.000000 4.000000 3.000000 0.000012 0.000002 0.00000416 2.000000 4.000000 3.000000 0.000003 0.000003 0.00000217 2.000000 4.000000 3.000000 0.000000 0.000001 0.00000018 2.000000 4.000000 3.000000 0.000000 0.000000 0.00000019 2.000000 4.000000 3.000000 0.000000 0.000000 0.00000020 2.000000 4.000000 3.000000 0.000000 0.000000 0.000000

dengan nilai awal P0 = (x0, y0, z0) = (1, 2, 2)

2 TENTUKAN SOLUSI SPL3x + y - z = 5

4x + 7y - 3z = 202x - 2y + 5z = 10dengan nilai awal P0 = x = y = z = 0x = 1,6063 y = 3,1328 z = 2,6504penyelesaian:

xr+1 = (5 - yr + zr)/3yr+1 = (20 - 4xr +3zr)/7zr+1 = (10 - 2xr + 2yr)/5

iterasi x y z Ԑx (%) Ԑy (%)0 0.000000 0.000000 0.000000 0.000000 0.0000001 1.666667 2.857143 2.000000 100.000000 100.0000002 1.380952 2.761905 2.476190 20.689655 3.4482763 1.571429 3.129252 2.552381 12.121212 11.7391304 1.474376 3.053061 2.623129 6.582590 2.4955445 1.523356 3.138840 2.631474 3.215243 2.7328276 1.497545 3.114428 2.646194 1.723586 0.7838377 1.510588 3.135486 2.646753 0.863501 0.6715998 1.503756 3.128272 2.649959 0.454376 0.2306009 1.507229 3.133551 2.649807 0.230431 0.168442

10 1.505419 3.131501 2.650529 0.120247 0.06546311 1.506343 3.132844 2.650433 0.061341 0.04289612 1.505863 3.132275 2.650601 0.031870 0.01816913 1.506108 3.132622 2.650565 0.016312 0.01105214 1.505981 3.132466 2.650605 0.008453 0.00497015 1.506046 3.132556 2.650594 0.004336 0.00287216 1.506013 3.132514 2.650604 0.002243 0.00134617 1.506030 3.132537 2.650600 0.001152 0.00075118 1.506021 3.132526 2.650603 0.000595 0.00036219 1.506026 3.132532 2.650602 0.000306 0.00019720 1.506023 3.132529 2.650603 0.000158 0.00009721 1.506025 3.132531 2.650602 0.000081 0.00005222 1.506024 3.132530 2.650602 0.000042 0.00002623 1.506024 3.132530 2.650602 0.000022 0.00001424 1.506024 3.132530 2.650602 0.000011 0.00000725 1.506024 3.132530 2.650602 0.000006 0.00000426 1.506024 3.132530 2.650602 0.000003 0.00000227 1.506024 3.132530 2.650602 0.000002 0.00000128 1.506024 3.132530 2.650602 0.000001 0.00000029 1.506024 3.132530 2.650602 0.000000 0.00000030 1.506024 3.132530 2.650602 0.000000 0.000000

Ԑz (%)0.000000

100.00000019.2307692.9850752.6970950.3171100.5562630.0211490.1209670.0057530.0272410.0036180.0063360.0013460.0015170.0004280.0003720.0001270.0000930.0000360.0000240.0000100.0000060.0000030.0000020.0000010.0000000.0000000.0000000.0000000.000000