1. KATHERINE LORENA SILVA ALONSOCODIGO: 2073612METODOS NUMERICOS-895985-633730<br />CALCULATION OF THE ROOT<br />Calculate the root of following: <br />For the methods: <br />a) Bisección<br />b) Falsa Posición<br />c) Secante<br />d) Newton-Raphson<br />e) Punto Fijo<br />We first make the graph of the function to get an inkling of what the value of the root and so allocate an appropriate interval to assess <br />Xf(X)010,10,718730750,20,470320050,30,248811640,40,049328960,5-0,132120560,6-0,298805790,7-0,453403040,8-0,598103480,9-0,73470111<br />Now with the help of Microsoft excel can do the calculation of the root for each method.<br />Down are the tables that are the result of this process and the respective root found, which is in a blue box. <br />BISECTION METHODN° ITERATIONXiXs Xr=Xi+Xs/2F(Xi)F(Xr)F(Xi)*F(Xr)Ea00211-0,86466472-0,86466472 1010,51-0,13212056-0,13212056100200,50,2510,356530660,3565306610030,250,50,3750,356530660,097366550,0347141633,333333340,3750,50,43750,09736655-0,02063798-0,0020094514,285714350,3750,43750,406250,097366550,037497310,003650987,6923076960,406250,43750,4218750,037497310,008219640,000308213,703703770,4218750,43750,42968750,00821964-0,00626086-5,1462E-051,8181818280,4218750,42968750,425781250,008219640,000966377,9432E-060,9174311990,425781250,42968750,4277343750,00096637-0,00265049-2,5613E-060,456621100,425781250,427734380,4267578130,00096637-0,00084287-8,1453E-070,22883295110,425781250,426757810,4262695310,000966376,1544E-055,9474E-080,11454754<br />FALSE POSITION METHODN° ITERACIONXiXs Xr=Xs-F(Xs)(Xi-Xs)/F(Xi)-F(Xs)F(Xi)F(Xs)F(Xr)F(Xi)*F(Xr)Ea0020,670761811-1,98168436-0,40931479-0,40931479 100,670761810,475948891-0,40931479-0,08994112-0,0899411240,93147915200,475948890,4366739461-0,08994112-0,01912266-0,019122668,994111954300,436673950,4284802651-0,01912266-0,00403004-0,004030041,912265637400,428480270,4267604051-0,00403004-0,00084767-0,000847670,403003816500,42676040,4263989581-0,00084767-0,00017823-0,000178230,084767304600,426398960,4263229761-0,00017823-3,7469E-05-3,7469E-050,017822515<br />NEWTON METHOD xiF(x)F´(x)ERROR01-0,86466472-1,270670566 10,319520940,20827694-2,055595758212,96853720,420842870,01014051-1,86196676424,075953930,4262892,5474E-05-1,8526289491,2775670940,426302751,612E-10-1,8526055020,003225450,426302750-1,8526055022,0411E-08<br />SECANTE METHOD Xi-1xiF(xi)F(xi-1)xi+1ERROR002-1,98168436110,67076181198,168436120,67076181-0,409314792-1,981684360,32473829106,55457920,670761810,324738290,197580806-0,409314790,4373896425,755376130,324738290,43738964-0,0204355940,197580810,426830352,4738832340,437389640,42683035-0,0009772-0,020435590,426300070,12439283<br />FIXED POINT METHODG1(x)N° ITERACIONESXF(x)G(x)101121-0,864664720,13533528330,135335280,627532490,76286776940,76286777-0,545406720,21746104750,217461050,429854050,64731509560,64731509-0,373315920,27399917370,273999170,304106650,5781058280,57810582-0,263429790,31467603190,314676030,218260970,532936999100,532937-0,18851030,344426695110,34442670,157724820,502151511120,50215151-0,135851660,366299849130,366299850,114357950,480657799140,4806578-0,098268320,382389484150,382389480,083047310,465436796160,4654368-0,071227610,394209182170,394209180,0603540,454563181180,45456318-0,051687140,402876038190,402876040,043875770,446751809200,44675181-0,037532320,40921949210,409219490,031900220,441119714220,44111971-0,027264640,413855074230,413855070,023193840,437048918<br />Plot a curve to compare the percentage of relative error versus the number of iterations of each method.<br />First we make the tables<br />NEWTON METHOD% ERROR RELATIVON° ITERACIONES 212,9685366124,0759539321,27756708930,00322540542,04108E-085 <br />SECANTE METHOD% ERROR RELATIVON° ITERACIONES 198,16843610106,5545793125,7553760722,47388323130,1243928264<br />BISECCION METHOD% ERROR RELATIVON° ITERACIONES 1000100133,33333333214,2857142937,69230769243,70370370451,81818181860,91743119370,45662100580,22883295290,11454753710<br />Now make de graph<br />
