Metodos numericos

Universidad Nacional Autónoma
de México

Facultad de Ingeniería

Materia: Análisis numérico

Alumno: Castillo Hdz. Yamil Hiram

Profesor: Ing. Alfonso Salazar Moreno

Semestre: 2015-1Grupo: 12

i

Biseccion

R. Falsa

N-R

X0

-0.5

-0.1608

0.4887

NO

X1

-0.25

-0.2327

-2.098

CONVERGE

X2

-0.375

-0.2864

0.1683

X3

-0.3125

-0.2812-0.568

X4

-0.2813

-0.2814

-0.33

X5

-0.2969

-0.2814

-0.283

X6

-0.2891

X7

-0.2852

X8

-0.2832

X9

-0.2822

X10

-0.2817

X11

-0.2815

X12-0.2814

-0.281

Aprox. S.

Memoria de cálculo.
F(X)

EXP(1-X)SIN(X)+1

[-1,0]

Metodo
Biseccion
Tabulacion
X

F(x)

-3
-2
-1
0
1
2
3

X0

-6.70489
-17.2637
-5.217681
1.841471
1.334512
1.019099

F(X)

Error

(-1+0)/2=
-0.5

intervalo

Exp(1-X0)
Sin(X0)+1
=-1.14864

[-.5,0]

X1
(-5+0)/2=
-.25

Exp(1-X0)
Sin(X0)+1
=0.136475

ABS(-.25-(-0.5))

[-.5,-.25]

Regla F.
Tabulacion
X

F(x)

-3
-2
-1
0
1
2
3

-6.70489
-17.2637
-5.21768
1
1.841471
1.334512
1.019099

X0

F(X)

0+[5.21768*(0+1)/ Exp(1-X0)(-5.21768-1)]
Sin(X0)+1
=-0.16083
=0.488741
X1
0.208893
-1.6083+
[0.488741
*(-.16083+1)/
(-5.21768 0.488741)]
=-0.2327

Error

Intervalo
[-1,0]

[-1,-.16083]
0.071873 [-1,-.2327]

N-R.Tabulacion

[-1,0]

X

F(x)

-3
-2
-1
0
1
2
3

-6.70489
-17.2637
-5.21768
1
1.841471
1.334512
1.019099

Convergencia
X0

(-1+0)/2
=-0.5

F(X)=

EXP(1-X)*SEN(X)+1F'(X)=

EXP(1-X)*[COS(X)-SEN(X)]

F''(X)=

-2

G'(X)=

F(X0)*F''(X0)/(F(X0))^2

G'(X)=

0.244283

Exp(1-x)COS(X)

Si converge.
X1
EXP(1 –X0)
*SEN(X0)+1=
-0.31113

ErrorABS(-.31113
+0.5)=0.188868

Aprox.S.
Tabulacion

[-1,0]

X

F(x)

-3
-2
-1
0
1
2
3

-6.70489
-17.2637
-5.21768
1
1.841471
1.334512
1.019099

F(X)=

EXP(1-X)*SEN(X)+1

G(X)=...