Jacobi Excel
3
CONTOH METODE ITERASI JACOBI 1 TENTUKAN SOLUSI SPL 4x - y + z = 7 4x - 8y +z = -21 (- 2x) + y + 5z = 15 solusi sejatinya adalah (2, 4, 3) penyelesaian: x r+1 = (7+ yr - zr)/4 yr+1 = (21 + 4xr + yr)/8 zr+1 = (15 + 2xr - yr)/5 iterasi x y z Ԑx (%) Ԑy (%) 0 1.000000 2.000000 2.000000 0.000000 0.000000 1 1.750000 3.375000 3.000000 42.857143 40.740741 2 1.843750 3.875000 3.025000 5.084746 12.903226 3 1.962500 3.925000 2.962500 6.050955 1.273885 4 1.990625 3.976563 3.000000 1.412873 1.296660 5 1.994141 3.995313 3.000938 0.176298 0.469300 6 1.998594 3.997188 2.998594 0.222813 0.046908 7 1.999648 3.999121 3.000000 0.052744 0.048350 8 1.999780 3.999824 3.000035 0.006593 0.017579 9 1.999947 3.999895 2.999947 0.008350 0.001758 10 1.999987 3.999967 3.000000 0.001978 0.001813 11 1.999992 3.999993 3.000001 0.000247 0.000659 12 1.999998 3.999996 2.999998 0.000313 0.000066 13 2.000000 3.999999 3.000000 0.000074 0.000068 14 2.000000 4.000000 3.000000 0.000009 0.000025 15 2.000000 4.000000 3.000000 0.000012 0.000002 16 2.000000 4.000000 3.000000 0.000003 0.000003 17 2.000000 4.000000 3.000000 0.000000 0.000001 18 2.000000 4.000000 3.000000 0.000000 0.000000 19 2.000000 4.000000 3.000000 0.000000 0.000000 20 2.000000 4.000000 3.000000 0.000000 0.000000 dengan nilai awal P0 = (x0, y0, z0) = (1, 2, 2)
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Transcript of Jacobi Excel
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
