metodos numèricos
28
MÉTODO DE LA BISECCIÓN i a b xi f(a) f(b) 0 -3 -2 -2.50000 -9.76102 1.61457 1 -2.5 -2 -2.25000 -3.66831 1.61457 2 -2.25 -2 -2.12500 -0.61392 1.61457 3 -2.25 -2.125 -2.18750 -0.61392 0.63025 4 -2.25 -2.1875 -2.21875 -0.61392 0.03808 5 -2.21875 -2.18750 -2.20313 -0.28084 0.03808 6 -2.20313 -2.18750 -2.19531 -0.11956 0.03808 7 -2.19531 -2.18750 -2.19141 -0.04028 0.03808 8 -2.19141 -2.18750 -2.18945 -0.00099 0.03808 9 -2.19141 -2.18945 -2.19043 -0.00099 0.01857 10 -2.19141 -2.19043 -2.19092 -0.00099 0.00880 11 -2.19141 -2.19092 -2.19116 -0.00099 0.00391 12 -2.19141 -2.19116 -2.19128 -0.00099 0.00146 13 -2.19141 -2.19128 -2.19135 -0.00099 0.00024 14 -2.19135 -2.19128 -2.19131 -0.00037 0.00024 15 -2.19131 -2.19128 -2.19130 -0.00007 0.00024 16 ### ### ### -0.00007 0.00009 MÉTODO DE LA BISECCIÓN i a b xi f(a) f(b) 0 -1 0 -0.50000 0.83229 -1.00000 1 -1 -0.5 -0.75000 0.83229 -0.79030 2 -1 -0.75 -0.87500 0.83229 -0.16861 3 -0.875 -0.75 -0.81250 0.29631 -0.16861 4 -0.8125 -0.75 -0.78125 0.05288 -0.16861 5 -0.81250 -0.78125 -0.79688 0.05288 -0.06081 6 -0.81250 -0.79688 -0.80469 0.05288 -0.00468 Iteracci ón Primer valor segundo valor Valor intermedi o Reemplaza "x" en la función con "a" Reemplaza "x" en la función con "b" Iteracci ón Primer valor segundo valor Aproximac ión de la raíz Reemplaza "x" en la función con "a" Reemplaza "x" en la función con "b"
description
Formulas para metodos numericos
Transcript of metodos numèricos
biseccinMTODO DE LA BISECCINf(a)*f(b)=-15.7598966014Tiene raizIteraccinPrimer valorsegundo valorValor intermedioReemplaza "x" en la funcin con "a"Reemplaza "x" en la funcin con "b"Reemplaza "x" en la funcin con "xi"Error iabxif(a)f(b)f(xi)|e|a-30-3-2-2.50000-9.761021.61457-3.668310.50000b-21-2.5-2-2.25000-3.668311.61457-0.613920.25000E0.000012-2.25-2-2.12500-0.613921.614570.630250.125003-2.25-2.125-2.18750-0.613920.630250.038080.062504-2.25-2.1875-2.21875-0.613920.03808-0.280840.031255-2.21875-2.18750-2.20313-0.280840.03808-0.119560.015636-2.20313-2.18750-2.19531-0.119560.03808-0.040280.007817-2.19531-2.18750-2.19141-0.040280.03808-0.000990.003918-2.19141-2.18750-2.18945-0.000990.038080.018570.001959-2.19141-2.18945-2.19043-0.000990.018570.008800.0009810-2.19141-2.19043-2.19092-0.000990.008800.003910.0004911-2.19141-2.19092-2.19116-0.000990.003910.001460.0002412-2.19141-2.19116-2.19128-0.000990.001460.000240.0001213-2.19141-2.19128-2.19135-0.000990.00024-0.000370.0000614-2.19135-2.19128-2.19131-0.000370.00024-0.000070.0000315-2.19131-2.19128-2.19130-0.000070.000240.000090.0000216-2.19131470-2.19129944-2.19130707-0.000070.000090.000010.00001
MTODO DE LA BISECCINf(a)*f(b)=-0.8322936731Tiene raizIteraccinPrimer valorsegundo valorAproximacin de la razReemplaza "x" en la funcin con "a"Reemplaza "x" en la funcin con "b"Reemplaza "x" en la funcin con "xi"Error Relativoiabxif(a)f(b)f(xi)|e|a-10-10-0.500000.83229-1.00000-0.790300.50000b01-1-0.5-0.750000.83229-0.79030-0.168610.25000E0.000012-1-0.75-0.875000.83229-0.168610.296310.125003-0.875-0.75-0.812500.29631-0.168610.052880.062504-0.8125-0.75-0.781250.05288-0.16861-0.060810.031255-0.81250-0.78125-0.796880.05288-0.06081-0.004680.015636-0.81250-0.79688-0.804690.05288-0.004680.023930.007817-0.80469-0.79688-0.800780.02393-0.004680.009580.003918-0.80078-0.79688-0.798830.00958-0.004680.002440.001959-0.79883-0.79688-0.797850.00244-0.00468-0.001120.0009810-0.79883-0.79785-0.798340.00244-0.001120.000660.0004911-0.79834-0.79785-0.798100.00066-0.00112-0.000230.0002412-0.79834-0.79810-0.798220.00066-0.000230.000210.0001213-0.79822-0.79810-0.798160.00021-0.00023-0.000010.0000614-0.79822-0.79816-0.798190.00021-0.000010.000100.0000315-0.79819-0.79816-0.798170.00010-0.000010.000040.0000216-0.798172-0.798157-0.7981640.00004-0.000010.000020.00001
MTODO DE LA BISECCINf(a)*f(b)=-0.8322936731Tiene raizIteraccinPrimer valorsegundo valorAproximacin de la razReemplaza "x" en la funcin con "a"Reemplaza "x" en la funcin con "b"Reemplaza "x" en la funcin con "xi"Error Relativoiabxif(a)f(b)f(xi)|e|a-10-10-0.500000.83229-1.00000-0.790300.50000b01-1-0.5-0.750000.83229-0.79030-0.168610.25000E0.000012-1-0.75-0.875000.83229-0.168610.296310.125003-0.875-0.75-0.812500.29631-0.168610.052880.062504-0.8125-0.75-0.781250.05288-0.16861-0.060810.031255-0.81250-0.78125-0.796880.05288-0.06081-0.004680.015636-0.81250-0.79688-0.804690.05288-0.004680.023930.007817-0.80469-0.79688-0.800780.02393-0.004680.009580.003918-0.80078-0.79688-0.798830.00958-0.004680.002440.001959-0.79883-0.79688-0.797850.00244-0.00468-0.001120.0009810-0.79883-0.79785-0.798340.00244-0.001120.000660.0004911-0.79834-0.79785-0.798100.00066-0.00112-0.000230.0002412-0.79834-0.79810-0.798220.00066-0.000230.000210.0001213-0.79822-0.79810-0.798160.00021-0.00023-0.000010.0000614-0.79822-0.79816-0.798190.00021-0.000010.000100.0000315-0.79819-0.79816-0.798170.00010-0.000010.000040.0000216-0.798172-0.798157-0.7981640.00004-0.000010.000020.00001MTODO DE LA BISECCINf(a)*f(b)=-5Tiene raizIteraccinPrimer valorsegundo valorAproximacin de la razReemplaza "x" en la funcin con "a"Reemplaza "x" en la funcin con "b"Reemplaza "x" en la funcin con "xi"Error Relativoiabxif(a)f(b)f(xi)|e|a-10121.50000-5.000001.00000-4.687500.50000b011.521.75000-4.687501.00000-2.808590.25000E0.0000121.7521.87500-2.808591.00000-1.187260.1250031.87521.93750-1.187261.00000-0.169910.0625041.937521.96875-0.169911.000000.395260.0312551.937501.968751.95313-0.169910.395260.107820.0156361.937501.953131.94531-0.169910.10782-0.032240.0078171.945311.953131.94922-0.032240.107820.037490.0039181.945311.949221.94727-0.032240.037490.002550.0019591.945311.947271.94629-0.032240.00255-0.014870.00098101.946291.947271.94678-0.014870.00255-0.006170.00049111.946781.947271.94702-0.006170.00255-0.001810.00024121.947021.947271.94714-0.001810.002550.000370.00012131.947021.947141.94708-0.001810.00037-0.000720.00006141.947081.947141.94711-0.000720.00037-0.000180.00003151.947111.947141.94713-0.000180.000370.000100.00002161.9471131.9471281.947121-0.000180.00010-0.000040.00001
Punto fijoE0.000001Xo3.5MTODO DEL PUNTO FIJO
xf(x)IteracinPunto xFuncin g(x)Funcin f(x)E absolutoCondicin5-2.8ixg(x)f(x)eC4-1.687503.52.4081632653-1.0918367347N/AN/A3-0.444444444412.40816326532.86218040790.45401714260.1586263191CONTINUA21.2522.86218040792.6103458489-0.2518345590.0964755529CONTINUA1632.61034584892.73379356910.12344772020.0451561967CONTINUA0ERROR:#DIV/0!42.73379356912.6690191809-0.06477438820.0242689856CONTINUA-1852.66901918092.7018860560.03286687520.0121644194CONTINUA-25.2562.7018860562.6849138436-0.01697221250.0063213248CONTINUA-35.555555555672.68491384362.69360033790.00868649430.0032248638CONTINUA-46.312582.69360033792.6891340179-0.004466320.0016608767CONTINUA-68.138888888992.68913401792.69142505210.00229103420.0008512346CONTINUA102.69142505212.6902484232-0.00117662890.0004373681CONTINUA112.69024842322.69085234060.00060391740.0002244335CONTINUA122.69085234062.6905422746-0.0003100660.0001152429CONTINUA132.69054227462.6907014440.00015916940.0000591554CONTINUA142.6907014442.690619729-0.0000817150.0000303703CONTINUA152.6906197292.69066167830.00004194930.0000155907CONTINUA162.69066167832.6906401427-0.00002153560.0000080039CONTINUA172.69064014272.69065119840.00001105570.0000041089CONTINUA182.69065119842.6906455227-0.00000567570.0000021094CONTINUA192.69064552272.69064843640.00000291370.0000010829CONTINUA202.69064843642.6906469406-0.00000149580.0000005559FINE0.00001Xo1MTODO DEL PUNTO FIJOcambio de signo
xf(x)IteracinPunto xFuncin g(x)Funcin f(x)E absolutoCondicin5547ixg(x)f(x)eC4205010.8164965809-5N/AN/A35110.81649658090.922958207-4.55555555560.1153482631CONTINUA2120.9229582070.870698651-4.82990397810.0600202561CONTINUA1-530.8706986510.8991217784-4.69960833950.0316120998CONTINUA0-340.89912177840.8843937939-4.77171706530.0166531974CONTINUA-1-550.88439379390.8922327144-4.73469479840.0087857353CONTINUA-2160.89223271440.8881174623-4.75449553080.00463368CONTINUA-35170.88811746230.8902938267-4.74412717430.0024445462CONTINUA-420580.89029382670.889147274-4.74961791830.0012894969CONTINUA-6118590.8891472740.8897525345-4.74672734260.0006802571CONTINUA100.88975253450.8894333629-4.7482538390.0003588482CONTINUA110.88943336290.8896017669-4.74744903210.0001893027CONTINUA120.88960176690.8895129387-4.74787371550.0000998616CONTINUA130.88951293870.8895598004-4.74764971980.0000526796CONTINUA140.88955980040.8895350804-4.74776789310.0000277898CONTINUA150.88953508040.889548121-4.74770555640.0000146598CONTINUA160.8895481210.8895412418-4.74773844140.0000077334FIN
Newto RE1.00E-05Xn3
IteracinValor de xFuncin evaluada en xDerivada de la funcin evaluada en xCociente de las funcion y la derivadaError AproximadoCondiciniXnf(Xn)f(Xn)f(Xn)/f(Xn)Xn+1e034150.26666666672.7333333333N/AN/A12.73333333330.478814814811.480.04170860762.69162472580.2666666667CONTINUAR22.69162472580.010713012610.96803209010.00097674882.69064797690.0417086076CONTINUAR32.69064797690.000005794710.95616769960.00000052892.6906474480.0009767488FINE1.00E-05Xn1MTODO DE NEWTON - RAPSHON
IteracinValor de xFuncin evaluada en xDerivada de la funcin evaluada en xCociente de las funcion y la derivadaError AproximadoCondiciniXnf(Xn)f(Xn)f(Xn)/f(Xn)Xn+1e010.459697691.84147098480.24963613220.7503638678N/AN/A10.75036386780.018923071.68190495290.01125097690.73911289090.2496361322CONTINUAR20.73911289090.000046461.67363254420.00002775750.73908513340.0112509769CONTINUAR30.73908513340.000000001.67361202930.00000000020.73908513320.0000277575FINE1.00E-05Xn1MTODO DE NEWTON - RAPSHON
IteracinValor de xFuncin evaluada en xDerivada de la funcin evaluada en xCociente de las funcion y la derivadaError AproximadoCondiciniXnf(Xn)f(Xn)f(Xn)/f(Xn)Xn+1e03.51.7755.750.30869565223.1913043478N/AN/A13.19130434780.3994019893.25761814740.12260552683.06869882110.3086956522CONTINUAR23.06869882110.05188045222.42635151040.02138208413.04731673690.1226055268CONTINUAR33.04731673690.00145603082.29061704220.000635653.04668108690.0213820841FIN
Interpolacin NewAPROXIMARPOLINOMIO INTERPOLADORf(x)0.45
los puntos dados para xFuncin evaluada en xiEcuacin de las diferencia divididas iXif(Xi)Xo=01-0.2911073085X1=0.60.8253356149-0.431086867-0.67908548880.0961090289X2=0.90.6216099683-0.3349778381-0.813076624X3=10.5403023059
APROXIMARPOLINOMIO INTERPOLADORf(x)0.45
los puntos dados para xFuncin evaluada en xiEcuacin de las diferencia divididas iXif(Xi)Xo=010.4415184401X1=0.61.2649110641-0.07022859590.3783127038X2=0.91.3784048752
APROXIMARf(x)0.45
los puntos dados para xFuncin evaluada en xiEcuacin de las diferencia divididas iXif(Xi)Xo=000.7833393821X1=0.60.4700036292-0.23389465810.5728341898X2=0.90.6418538862APROXIMARf(x)0.45
los puntos dados para xFuncin evaluada en xiEcuacin de las diferencia divididas iXif(Xi)Xo=001.1402280139X1=0.60.68413680830.86649261131.920071364X2=0.91.2601582176
Int lagrangelos puntos dados para xFuncin evaluada en xiLoiXif(Xi)x--0.5x--0.25x-0Xo=-0.75-0.0718125-0.09375X1=-0.5-0.02475L1X2=-0.250.33499375x--0.75x--0.25x-0X3=01.1010.03125L2x--0.75x--0.5x-0-0.03125L3x--0.75x--0.5x--0.250.09375
Graficaxf(x)45.93.94.8593.83.9323.250.6031253-0.12.75-0.4281252.5-0.4752.25-0.3343752-0.11.750.1343751.50.2751.250.2281251-0.10.75-0.8031250.5-1.9750.25-3.7093750-6.1-0.25-9.240625-0.5-13.225-0.75-18.146875-1-24.1-1.25-31.178125
xf(x)3.1250.198828133.10.1313.0750.067296883.050.0076253.025-0.048109383-0.12.975-0.148140632.95-0.1926252.925-0.233546882.9-0.2712.875-0.30507813
SecanteXi3.5Xi-12.5Ea0.00001
Iteracinvalores dadosValor presente menos valoir anteriorFuncion evaluada en el valor presenteFuncion evaluada en el valor anteriorError AproximadoCondicini Xi(Xi)-(Xi-1)f(Xi)f(Xi-1)eC02.513.511.775-0.4751CONTINUAR22.7111111111-0.7888888889-0.45151714681.7750.7888888889CONTINUAR32.87109050350.1599793924-0.3101081921-0.45151714680.1599793924CONTINUAR43.22192344940.3508329460.5025266849-0.31010819210.350832946FIN2.7111111111
Secante modificadoXi3.5d0.03Ea0.00001
i Xid*Xi*f(Xi)f(Xi)xi+d*xif(xi+d*xi)eC03.50.1863751.7753.6052.42952012513.21524939740.04624834390.47946870443.31170687930.84518310230.2847506026CONTINUAR23.08878912090.00944509110.10192873553.18145279450.36765529340.1264602765CONTINUAR33.05324472080.00138727760.01514539143.14484206250.2556604680.0355444001CONTINUAR43.04747677640.00016663910.00182270063.13890107970.23836257870.0057679444ERROR:#REF!
