Plan1unifacs - universidade salvador - campus fsadata: 22/05/15disciplina: clculo numricoprof.: marcelo pedreira da silvamtodos iterativos para a soluo de sistemas lineares1.0conceitos gerais dos mtodos iterativos1.1procedimentos gerais1.1.1explicitao das equaes do sistema linear, colocando suas incgnitas em funo das demais incgnitas;

a11x1+a12x2+a13x3=b1x1=[b1-(a12x2+a13x3)]/a11a21x1+a22x2+a23x3=b2x2=[b2-(a21x1+a23x3)]/a22a31x1+a32x2+a33x3=b3x3=[b3-(a31x1+a32x2)]/a33

1.1.2atribuio de valores iniciais para as incgnitas

1.1.3iterao 1 1.1.3.1os valores iniciais so substituidos1.1.3.2novos valores estimados so calculados

1.1.4iterao 2 1.1.4.1os valores resultantes da iterao 1 so substituidos1.1.4.2novos valores estimados so calculados

1.1.5iterao 3... at atingir critrio de parada!

1.2critrio de convergncia/parada

exemplo:

3.0000002.000000-1.0000008.0000001.500000a = 2.000000-4.0000002.000000b = -4.000000x =2.000000-1.0000001.0000005.0000003.0000000.500000

2.0mtodo de jacobi

itx1e1x2e2x3e300.0000000.0000000.00000012.666667100.0000001.000000100.0000000.600000100.00000022.20000021.2121212.63333362.0253160.93333335.71428631.22222280.0000002.5666672.5974030.51333381.81818241.1266678.4812621.86777837.4182030.33111155.03355751.53185226.4506771.7288898.0334190.45177826.70929761.6646677.9784631.99181513.2003200.56059319.41067771.5256549.1116542.1126305.7186940.5345704.86787681.4364376.2110132.0301124.0646660.48260510.76769691.4741272.5567481.9595213.6024800.4812650.278433101.5207413.0652321.9776960.9189910.5029214.306085111.5158430.3231092.0118311.6967240.5086091.118320121.4949821.3953922.0122260.0196310.5008021.558821131.4921170.1920461.9978920.7174430.4965510.856140141.5002560.5424921.9943340.1784240.4988450.459790151.5033920.2086471.9995500.2608690.5011840.466780161.5006950.1797612.0022880.1367490.5007680.083049171.4987310.1310462.0007320.0778100.4996810.217569181.4994060.0450491.9992060.0763100.4996000.016304191.5003960.0659771.9995030.0148540.5000400.088035201.5003450.0034172.0002180.0357490.5001790.027706211.4999140.0287032.0002620.0021830.5000250.030652221.4998340.0053471.9999700.0145950.4999310.018969231.4999970.0108651.9998820.0043760.4999730.008468241.5000690.0048301.9999850.0051330.5000230.010019251.5000180.0034492.0000460.0030640.5000170.001208261.4999750.0028582.0000170.0014450.4999940.004521271.4999870.0007821.9999850.0016370.4999920.000559281.5000070.0013931.9999890.0002230.5000000.001778291.5000070.0000012.0000040.0007450.5000040.000657301.4999990.0005892.0000060.0000820.5000010.0005963.0mtodo de gauss-seidel

itx1e1x2e2x3e300.0000000.0000000.00000012.666667100.0000002.333333100.0000000.666667100.00000021.333333100.0000002.00000016.6666670.46666742.85714331.48888910.4477611.9777781.1235960.5022227.07964641.5155561.7595312.0088891.5486730.5013330.17730551.4945191.4076131.9979260.5487170.4993190.40351361.5011560.4421292.0002370.1155420.5001840.17297371.4999030.0834952.0000430.0096790.4999720.04235381.4999620.0038981.9999670.0038320.4999990.00540491.5000220.0040072.0000100.0021780.5000020.000662101.4999940.0018631.9999980.0006160.5000020.000000111.5000020.0005472.0000020.0002050.4999990.000625

Plan2

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