optimizacion empleando metodos numericos, Ejercicios de Métodos Numéricos

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A) f(x)=-x^2+8x-12 f(x)=-2x+8^ X= B) n x0 f(0) x1 f(1) x2 f(2) 1 0 -12 2 0 6 0 2 4 4 0 -12 6 0 3 4 4 0 5 0

x3 f(3) (^1 384 0 ) (^4 4 2 96 0 ) 4 4 1 2 3 1 -144 -240 0 2 -48 -48 0

f(X) -1.5^6-2x^4+12x f´(X) -9x^5-8x^3+ f´´(X) -45x^4-24x^ n xi xi+1 Ea 0 6 - 1 -120933210 -120933209 -1.2251E- 2 -120933209 -120933209 -4.5653E- 3 -120933209 -120933209 -3.9428E- 4 -120933209 -120933209 -2.9843E- 5 -120933209 -120933209 0 x

f(x1) xu f(xu) d 930083747864 2 30744 1. 5.047876E+25 2 30744 0. 3.606262E+19 1.52786405 2097.87956 0.

f(X) -1.5^6-2x^4+12x f´(X) -9x^5-8x^3+ f´´(X) -45x^4-24x^ n xi xi+1 Ea 0 2 -18526. 1 -18526.0167 -18525.9718 -2.4192E- 2 -18525.9718 -18525.9719 -1.6179E- 3 -18525.9719 -18525.9719 0

i xl f(xl) x2 f(x2)

d)

f(x)=-x^4-2x^3-8x^2-5x f´(x)=4x^3-6x^2-16x-

a i xl f(xl) x2 f(x2) 1 -2 30696 -0.85410197 -4. 2 -0.85410197 0.65689588 -0.14589803 -1. 3 -0.85410197 0.65689588 -0.41640786 -4. b i xl f(xl) x2 f(x2) 1 -1 18 -0.23606798 -2. 2 -0.23606798 0.97226512 0.23606798 2. 3 -0.23606798 0.97226512 0.05572809 0. 4 -0.23606798 0.97226512 -0.05572809 -0. c f(X) -x^4-2x^3-8x^2-5x f´(X) -4x^3-6x^2-16x- f´´(X) -12x^2-12x- n xi xi+1 Ea 0 -1 39. 1 39.3125-2253536877 - 2 -2253536877 1.3949E+48 1

x1 f(x1) xu f(xu) d

• i xl f(xl) x2 f(x2) x
  • 1 0 0 0.76393202 11.1979901 1.
  • 2 0.76393202 11.1979901 1.23606798 264.605424 1.
  • 3 0.76393202 11.1979901 1.05572809 64.2678251 1.
• i xl f(xl) x2 f(x2) x
  • 1 1 42 1.38196601 778.8291 1.
  • 2 1.38196601 778.8291 1.61803399 3709.17249 1.
  • 3 1.38196601 778.8291 1.52786405 2097.87956 1.
• a) f(x)=4x-1.8x^2+1.2^3-0.3^ - 1 2 20 2.76393202250 32. - 2 2.76393202 32.6362146 2.94427191000 35. - 3 2.76393202 32.6362146 2.87538820250 34. - 4 2.8753882 34.4044159 2.90169943749 34. - 5 2.90169944 34.8126166 2.90791067753 34. - 6 2.90791068 34.9084012 2.90937695240 34. - 7 2.90937695 34.9309797 2.90972309294 34. - 8 2.90972309 34.9363079 2.90980480564 34. - 9 2.90980481 34.9375657 2.90982409539 34.
  • 10 2.9098241 34.9378626 2.90982864908 34.
  • 11 2.90982865 34.9379326 2.90982972406 34.
  • 12 2.90982972 34.9379492 2.90982997783 34.
  • 13 2.90982998 34.9379531 2.90983003774 34.
  • 14 2.90983004 34.937954 2.90983005188 34.
    • 1 1.75 16.1300781 n x0 f(x0) x1 f(x1)
    • 2 2 20 -3.4859307359 -87.
    • 3 3 36.3 1.92485634261 18.
    • 4 4 44.8 3.02435200281 36. - f(x)=4x-1.8x^2+1.2^3-
      • c) f´(x)=4-3,6x-3,6x^2-1,
• 3.23606798 39.5606798 4 44.8 1.23606798 x1 f(x1) xu f(xu) d n xi
• 3.05572809 37.1131772 3.23606798 39.5606798 0.29179607 1 1.
• 2.94427191 35.4644565 3.05572809 37.1131772 0.18033989 2 1.
• 2.91796068 35.0629 2.94427191 35.4644565 0.04257247 3 0.
• 2.91174943 34.9674856 2.91796068 35.0629 0.
• 2.91028316 34.9449277 2.91174943 34.9674856 0.
• 2.90993702 34.9396006 2.91028316 34.9449277 0.
• 2.90985531 34.9383429 2.90993702 34.9396006 0.
• 2.90983602 34.938046 2.90985531 34.9383429 3.12115E-
• 2.90983146 34.937976 2.90983602 34.938046 7.36803E-
• 2.90983039 34.9379594 2.90983146 34.937976 1.73936E-
• 2.90983013 34.9379555 2.90983039 34.9379594 4.10606E-
• 2.90983007 34.9379546 2.90983013 34.9379555 9.6931E-
• 2.90983006 34.9379544 2.90983007 34.9379546 2.28823E-
  • 2.5 28.28125 -3.48593074 -87.2019149 -36.2926758 63.75 -26.5136719 -16. x2 f(x2) x3 f(x3) f(x0)(x1^2-x2^2)f(x1)(x2^2-x0^2)f(x2)(x0^2-x1^2)2*f(x0)(x1-x2)
    • 6 -40.8 1.92485634 18.8083649 -476.965738 -2790.46128 332.589894 -379.
    • 7 -192.5 3.024352 36.65824 -1644.20589 752.334596 -1019.27365 -368.
    • 8 -467.2 3.66444295 43.7819202 -2457.42761 1759.59552 -3201.85941 -445.
• f(x)=4x-1.8x^2+1.2^3-0.3^
  • f´(x)=4-3,6x-3,6x^2-1,2x^
    • f´´(x)=-3,6-7,2x-3,6x^ - -71.6 -57.6 1. f´(x) f´´(x) xi+1 Ea
      • -19.9457903 -27.3626736 1.02800287 -70.
      • -4.80891366 -14.8060643 0.70320936 -46.
      • -0.72905323 -10.4433196 0.63339887 -11. - 30 -14. 2f(x1)(x2-x0)2f(x2)(x0-x1)
      • -697.615319 -447.
        • 150.466919 -413.
          • 293.26592 -911.
• -0.14589803 35767547 1 42 1.
  • 0.29179607 8096.59316 1 42 1.
• -0.14589803 288425751 0.29179607 3.50168706
  • 0.23606798 998309.029 1 42 1. x1 f(x1) xu f(xu) d
  • 0.52786405 998490.677 1 42 0.
  • 0.23606798 8.5614754 0.52786405 6.38475827
  • 0.05572809 -7.48821452 0.23606798 2.83283185
  • 1 0.1 30.2 0.5 7 5 10. n x0 f(x0) x1 f(x1) x2 f(x2)
  • 2 2 5.5 2.71666667 31.8703222 6 12.
  • 3 3 7 4.08197607 44.6477495 7 14.
  • 4 4 8.75 5.08226291 24.2007907 8 16.
  • 5 5 10.6 6.22481327 -66.3419178 9 18.
  • 6 6 12.5 6.95857033 -184.070021 10 20.
  • 7 7 14.4285714 7.98567552 -462.186577 11 22.
  • 8 8 16.375 8.99391228 -908.375369 12 24.
  • 9 9 18.3333333 9.99682629 -1577.46246 13 26.
• 10 10 20.3 10.9981504 -2531.23272 14 28.
• 2.71666667 6.53762781 -747.45 174.93 -2.544 -271.8 68.6 -8. x3 f(x3) f(x0)(x1^2-x2^2)f(x1)(x2^2-x0^2)f(x2)(x0^2-x1^2)2f(x0)(x1-x2)2f(x1)(x2-x0)2*f(x2)(x0-x1)
• 4.08197607 8.8988903 -157.408472 1019.85031 -42.2534722 -36.1166667 254.962578 -17.
• 5.08226291 10.754814 -226.3623 1785.90998 -110.559341 -40.8523351 357.181996 -31.
• 6.22481327 12.9315687 -333.992783 1161.63795 -160.956363 -51.0603992 193.606325 -35.
• 6.95857033 14.3482637 -447.868017 -3715.1474 -252.052171 -58.8339587 -530.735343 -44.
• 7.98567552 16.3470237 -644.728737 -11780.4814 -252.160531 -76.0357418 -1472.56017 -38.
• 8.99391228 18.3213835 -825.732519 -33277.4336 -328.990756 -86.9847921 -3697.49262 -43.
• 9.99682629 20.2937478 -1033.41875 -72670.0295 -409.593609 -98.4493728 -7267.00295 -48.
• 10.9981504 22.2690739 -1266.16351 -138816.697 -496.7199 -110.11637 -12619.6997 -52.
• 11.9988392 24.2477025 -1523.32597 -242998.341 -591.352008 -121.875095 -20249.8618 -56.

*f(x2)(x0-x1)