Xi                     f(Xi)          f'(Xi)       X(i+1)          Xi              f(xi)          f''(Xi)
           1    ...
X(i+1)         Xi              f(xi)          f''(Xi)         X(i+1)              Xi             f'(xi)
          -69.2263...
f''(x)          X(i+1)
          -0.01346746      18.0295028
            -0.0070409    -4.69329033
            0.00101742 ...
X           g(x)       Error          X
                 1           6          0                2
                 6     ...
h(x)           Error
 1.29099445               0
 1.37477412     6.09406791
 1.36401734     0.78860996
 1.36538433     0.1...
f(Xi)*f(Xs)=                -100
Biseccion
Iteraciones       Xi                  Xr                Xs               f(Xi) ...
6        0.427457486 -0.00213813 0.04418695 0.42631535        5.78906073
              7        0.426315346 -2.3333E-05 -0...
21   0.446751809    0.40921949   9.82106159
22    0.40921949   0.441119714    9.1716841
23   0.441119714   0.413855074    ...
Falsa Posicion                f(Xi)*f(Xs)=
      f(Xi)*f(Xr)      Error         Iteraciones Xi                Xr
         ...
7   0.42630275        0
                                                            8   0.42630275        0
              ...
Xs             f(Xi)        f(Xr)           f(Xs)          f(Xi)*f(Xr)     Error
         100            1    -0.85205711 ...
-1.8526055   0.42630275   6.6082E-09
          -1.8526055   0.42630275            0
          -1.8526055   0.42630275     ...
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  1. 1. Xi f(Xi) f'(Xi) X(i+1) Xi f(xi) f''(Xi) 1 -0.01846518 -0.1849452 0.90015866 1 -0.01846518 -0.00026294 0.90015866 -0.01662868 -0.18496866 0.81025867 -69.226367 -25.9878513 0.00074302 0.81025867 -0.01497314 -0.18498773 0.7293174 34906.7514 -7.1125E+13 -9.7399E+33 0.7293174 -0.01348118 -0.18500323 0.65644742 34906.7514 -7.1125E+13 -9.7399E+33 0.65644742 -0.01213698 -0.18501582 0.59084775 34906.7514 -7.1125E+13 -9.7399E+33 0.59084775 -0.01092614 -0.18502605 0.53179587 34906.7514 -7.1125E+13 -9.7399E+33 0.53179587 -0.00983561 -0.18503435 0.47864029 34906.7514 -7.1125E+13 -9.7399E+33 0.47864029 -0.00885357 -0.18504109 0.43079377 34906.7514 -7.1125E+13 -9.7399E+33 0.43079377 -0.00796933 -0.18504656 0.38772717 34906.7514 -7.1125E+13 -9.7399E+33 0.38772717 -0.00717321 -0.18505099 0.34896378 34906.7514 -7.1125E+13 -9.7399E+33 0.34896378 -0.00645648 -0.18505459 0.3140742 34906.7514 -7.1125E+13 -9.7399E+33 0.3140742 -0.00581126 -0.18505751 0.28267174 34906.7514 -7.1125E+13 -9.7399E+33 0.28267174 -0.00523045 -0.18505987 0.25440818 34906.7514 -7.1125E+13 -9.7399E+33 0.25440818 -0.00470764 -0.18506179 0.22897 34906.7514 -7.1125E+13 -9.7399E+33 0.22897 -0.00423704 -0.18506335 0.20607492 34906.7514 -7.1125E+13 -9.7399E+33 0.20607492 -0.00381346 -0.18506461 0.18546883 34906.7514 -7.1125E+13 -9.7399E+33 0.18546883 -0.0034322 -0.18506563 0.16692297 34906.7514 -7.1125E+13 -9.7399E+33 0.16692297 -0.00308905 -0.18506646 0.15023142 34906.7514 -7.1125E+13 -9.7399E+33 0.15023142 -0.00278019 -0.18506713 0.13520882 34906.7514 -7.1125E+13 -9.7399E+33 0.13520882 -0.0025022 -0.18506768 0.12168834 34906.7514 -7.1125E+13 -9.7399E+33 0.12168834 -0.00225201 -0.18506812 0.10951979 34906.7514 -7.1125E+13 -9.7399E+33 En esta primera iteracion En la segunda realizamos Metodo Newton Metodo Newton Raphson Raphson aplicamos el metodo de el metodo utilizando de forma tradicional sin la segunda derivada en alterar la formulacion vez de la primera, donde del metodo el valor si converge en la tercera iteracion pero en funcion de el valor de f(x)
  2. 2. X(i+1) Xi f(xi) f''(Xi) X(i+1) Xi f'(xi) -69.226367 1 -0.01846518 -0.00026294 -69.226367 29 -0.14774472 34906.7514 -69.226367 -25.9878513 0.00074302 34906.7514 18.0295028 -0.15998881 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -4.69329033 -0.18198938 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 174.179507 -16.6590845 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 58.717223 -0.36641024 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 48.8399257 -0.23047613 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 40.7239649 -0.17254591 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 32.8212599 -0.14997112 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 23.4693241 -0.15141027 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 8.39475203 -0.17769881 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -57.6995945 0.67690603 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -18.2213735 -0.12734502 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 51.6162525 -0.26056247 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 43.1481608 -0.18562151 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 35.3270954 -0.15419792 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 26.6673166 -0.14845466 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 14.2752606 -0.16713717 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 -17.9127124 -0.12952419 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 52.3954856 -0.27007642 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 43.8070154 -0.18975813 34906.7514 34906.7514 -7.1125E+13 -9.7399E+33 34906.7514 35.9848724 -0.15572251 ealizamos En este recuadro En este metododo Metodo Newton Metodo Newton Raphson Raphson ando de encontramos que si la remplazamos a f(x) por vada en funcion la hacemos f'(xi) y a f'(x) por ra, donde utilizando la segunda f''(xi), de igual manera erge en la derivada en vez de la los resultados no son los n pero en primera pero en funcion esperados para ninguna alor de de Xi, el valor es combinacion, exepto la divergente segunda q por obvias monotonicamente razones no es la correcta
  3. 3. f''(x) X(i+1) -0.01346746 18.0295028 -0.0070409 -4.69329033 0.00101742 174.179507 -0.14428161 58.717223 -0.0370962 48.8399257 -0.02839789 40.7239649 -0.02183378 32.8212599 -0.01603637 23.4693241 -0.01004408 8.39475203 -0.00268856 -57.6995945 -0.01714632 -18.2213735 0.00182344 51.6162525 -0.03076992 43.1481608 -0.02373353 35.3270954 -0.01780622 26.6673166 -0.01197983 14.2752606 -0.00519253 -17.9127124 0.00184223 52.3954856 -0.03144639 43.8070154 -0.0242591 35.9848724 -0.0182816 27.46688 tododo os a f(x) por ual manera dos no son los para ninguna on, exepto la por obvias es la correcta
  4. 4. X g(x) Error X 1 6 0 2 6 -344 101.744186 1.29099445 -344 40233906 100.000855 1.37477412 40233906 -6.5129E+22 100 1.36401734 -6.5129E+22 2.7627E+68 100 1.36538433 2.7627E+68 -2.109E+205 100 1.36521038 -2.109E+205 #NUM! #NUM! 1.36523251 #NUM! #NUM! #NUM! 1.3652297 #NUM! #NUM! #NUM! 1.36523005 #NUM! #NUM! #NUM! 1.36523001 1.36523001 1.36523001 1.36523001 Se quiere aproximar una raíz de la 1.36523001 ecuación x3 - 30x2 + 2400 = 0, que 1.36523001 sabemos se encuentra en el intervalo 1.36523001 1.36523001 (10,15), mediante el método del 1.36523001 punto fijo. ¿Cuál de las siguientes 1.36523001 funciones utilizarías para poder 1.36523001 1.36523001 esperar convergencia en el proceso de 1.36523001 iteración? Justifique su respuesta. 1.36523001
  5. 5. h(x) Error 1.29099445 0 1.37477412 6.09406791 1.36401734 0.78860996 1.36538433 0.10011736 1.36521038 0.01274138 1.36523251 0.00162102 1.3652297 0.00020624 1.36523005 2.624E-05 1.36523001 3.3385E-06 1.36523001 4.2476E-07 1.36523001 5.4042E-08 1.36523001 6.8757E-09 1.36523001 8.7479E-10 1.36523001 1.113E-10 1.36523001 1.4166E-11 1.36523001 1.8053E-12 1.36523001 2.277E-13 1.36523001 3.2529E-14 1.36523001 0 1.36523001 0 1.36523001 0 1.36523001 0 1.36523001 0
  6. 6. f(Xi)*f(Xs)= -100 Biseccion Iteraciones Xi Xr Xs f(Xi) f(Xr) 1 0 50 100 1 -50 2 0 25 50 1 -25 3 0 12.5 25 1 -12.5 4 0 6.25 12.5 1 -6.24999627 5 0 3.125 6.25 1 -3.12306955 6 0 1.5625 3.125 1 -1.51856307 7 0 0.78125 1.5625 1 -0.57163861 8 0 0.390625 0.78125 1 0.06720836 9 0.390625 0.5859375 0.78125 0.06720836 -0.27615195 10 0.390625 0.48828125 0.5859375 0.06720836 -0.1116778 11 0.390625 0.439453125 0.48828125 0.06720836 -0.0242163 12 0.390625 0.415039063 0.43945313 0.06720836 0.02097616 13 0.415039063 0.427246094 0.43945313 0.02097616 -0.00174688 14 0.415039063 0.421142578 0.42724609 0.02097616 0.00958255 15 0.421142578 0.424194336 0.42724609 0.00958255 0.00390986 Grafica Biseccion Biseccion 120 100 80 60 Error vs Iteraciones 40 20 0 0 5 10 15 20 Secante Iteracion Xi f(Xi) f(Xi-1) Xi+1 Error 0 110 -110 1 100 -100 -110 0 0 2 0 1 -100 0.99009901 #DIV/0! 3 0.99009901 -0.85205711 1 0.53459421 100 4 0.534594211 -0.1913072 -0.85205711 0.40271171 85.205711 5 0.402711712 0.044186946 -0.1913072 0.42745749 32.7486126
  7. 7. 6 0.427457486 -0.00213813 0.04418695 0.42631535 5.78906073 7 0.426315346 -2.3333E-05 -0.00213813 0.42630274 0.26790971 8 0.426302744 1.23969E-08 -2.3333E-05 0.42630275 0.00295596 9 0.426302751 -7.1942E-14 1.2397E-08 0.42630275 1.5697E-06 Grafico Secante Secante 120 100 80 60 Error vs Iteraciones 40 20 0 0 2 4 6 8 10 -20 Punto Fijo Iteracion Xi f(x) Error 1 100 1.3839E-87 0 2 1.3839E-87 1 7.226E+90 8E+90 3 1 0.135335283 100 4 0.135335283 0.762867769 638.90561 7E+90 5 0.762867769 0.217461047 82.2596669 6E+90 6 0.217461047 0.647315095 250.806629 5E+90 7 0.647315095 0.273999173 66.4056888 8 0.273999173 0.57810582 136.247098 4E+90 9 0.57810582 0.314676031 52.603976 3E+90 10 0.314676031 0.532936999 83.7146025 11 0.532936999 0.344426695 40.9543657 2E+90 12 0.344426695 0.502151511 54.7316182 1E+90 13 0.502151511 0.366299849 31.4098061 14 0.366299849 0.480657799 37.0875562 0 15 0.480657799 0.382389484 23.7919682 -1E+90 0 16 0.382389484 0.465436796 25.6984881 17 0.465436796 0.394209182 17.8428765 18 0.394209182 0.454563181 18.0684819 19 0.454563181 0.402876038 13.277362 20 0.402876038 0.446751809 12.82954
  8. 8. 21 0.446751809 0.40921949 9.82106159 22 0.40921949 0.441119714 9.1716841 23 0.441119714 0.413855074 7.2316479 24 0.413855074 0.437048918 6.58796803 25 0.437048918 0.417238267 5.30692176 26 0.417238267 0.43410166 4.74804282 27 0.43410166 0.419704948 3.8846644 28 0.419704948 0.431965353 3.43019816 29 0.431965353 0.421502022 2.83828423 30 0.421502022 0.430415592 2.48239164 31 0.430415592 0.422810503 2.07092188 32 0.422810503 0.429290684 1.79869933 33 0.429290684 0.42376282 1.50950888 34 0.42376282 0.42847382 1.30447115 35 0.42847382 0.424455699 1.09948375 36 0.424455699 0.42788047 0.94665268
  9. 9. Falsa Posicion f(Xi)*f(Xs)= f(Xi)*f(Xr) Error Iteraciones Xi Xr -50 0 1 0 0.99009901 -25 100 2 0 0.534594211 -12.5 100 3 0 0.44874589 -6.24999627 100 4 0 0.431007689 -3.12306955 100 5 0 0.427291289 -1.51856307 100 6 0 0.426510545 -0.57163861 100 7 0 0.426346434 0.06720836 100 8 0 0.426311934 -0.01855972 33.3333333 9 0 0.426304682 -0.00750568 20 10 0 0.426303157 -0.00162754 11.1111111 11 0 0.426302836 0.00140977 5.88235294 12 0 0.426302769 -3.6643E-05 2.85714286 13 0 0.426302755 0.000201 1.44927536 14 0 0.426302752 3.7466E-05 0.71942446 15 0 0.426302751 Grafica Falsa Posicion 90 80 70 60 50 40 Error vs Iteraciones 30 20 10 0 0 5 Newton Raphson Iteracion Xi f(Xi) 1 100 -100 2 0 1 3 0.33333333 0.180083786 4 0.42218312 0.007646564 5 0.42629493 1.44945E-05 6 0.42630275 5.21899E-11
  10. 10. 7 0.42630275 0 8 0.42630275 0 9 0.42630275 0 10 0.42630275 0 Grafica Newton Raphson Newton Raphson 120 100 80 60 Error vs Iteraciones 40 20 0 0 2 4 6 8 -20 Punto Fijo Error vs Iteraciones 10 20 30 40
  11. 11. Xs f(Xi) f(Xr) f(Xs) f(Xi)*f(Xr) Error 100 1 -0.85205711 -100 -0.85205711 0 0.99009901 1 -0.1913072 -0.85205711 -0.1913072 85.205711 0.53459421 1 -0.04115518 -0.1913072 -0.04115518 19.1307203 0.44874589 1 -0.00869758 -0.04115518 -0.00869758 4.11551845 0.43100769 1 -0.00183054 -0.00869758 -0.00183054 0.86975798 0.42729129 1 -0.00038492 -0.00183054 -0.00038492 0.18305385 0.42651055 1 -8.0926E-05 -0.00038492 -8.0926E-05 0.03849237 0.42634643 1 -1.7013E-05 -8.0926E-05 -1.7013E-05 0.00809262 0.42631193 1 -3.5767E-06 -1.7013E-05 -3.5767E-06 0.00170132 0.42630468 1 -7.5192E-07 -3.5767E-06 -7.5192E-07 0.00035767 0.42630316 1 -1.5808E-07 -7.5192E-07 -1.5808E-07 7.5192E-05 0.42630284 1 -3.3232E-08 -1.5808E-07 -3.3232E-08 1.5808E-05 0.42630277 1 -6.9864E-09 -3.3232E-08 -6.9864E-09 3.3232E-06 0.42630275 1 -1.4687E-09 -6.9864E-09 -1.4687E-09 6.9864E-07 0.42630275 1 -3.0877E-10 -1.4687E-09 -3.0877E-10 1.4687E-07 Falsa Posicion Error vs Iteraciones 10 15 20 f'(Xi) Xi+1 Error -1 0 0 -3 0.33333333 #DIV/0! -2.02683424 0.42218312 100 -1.85965936 0.42629493 21.0453192 -1.85261884 0.42630275 0.96454564 -1.8526055 0.42630275 0.00183526
  12. 12. -1.8526055 0.42630275 6.6082E-09 -1.8526055 0.42630275 0 -1.8526055 0.42630275 0 -1.8526055 0.42630275 0 Newton Raphson Error vs Iteraciones 8 10 12 Biseccion 120 100 80 Newton Raphson 60 Secante 40 Falsa Posicion Biseccion 20 0 0 5 10 15 20 -20

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