8/17/2019 p01!12!2Soluciones de Ecuaciones No Lineales
1/4
†
†
• x3 − 2x − 5 = 0• e−x = x
• x
· sin(x) = 1
• x3 − 3x2 + 3x − 1 = 0
(0, 16)
• x cos(x) = ln(x)• 2x − e−x = 0• e−2x = 1 − x
† 0.02
p(x) := x3+94x2
−389x+294
x0 = 2
p
a
f (x) = x2−a
f
xn+1 =
12(xn+
a
xn)
n ≥ 0
x0 >
√ a
xn+1 < xn n ≥ 0
n
a
n ∈N
n ≥ 2
8/17/2019 p01!12!2Soluciones de Ecuaciones No Lineales
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†
g(x) = x
5
6
g(x) = x
2
4 − 32x + 54 [0, 1]
g(x) = cos(x)+sen(x)2
g(x) = x2 − 2x + 23
f : R→ R
f (x) :=
sgn(x) e−
1
x2
x = 0
0
x = 0
†
x0 f
†
xn+1 = f (xn)
x3 + 4x2 − 10 = 0 [1, 2]
x = g(x)
g
g(x)
g(x) = x − x3 − 4x2 + 10
g(x) = (10
x − 4x) 12
g(x) = 12(10 − x3)1
2
g(x) = ( 104+x )
1
2
g(x) = x − x3+4x2−10
3x2+8x
g
[1, 2]
† x0 = 1.5
xn =
2 +
2 +
· · · + √ 2
n ≥ 1
n
g
xn+1 = g(xn) n ≥ 1
xn+1 = g(xn) n ≥ 0
x0 = 1.5
g(x) = x2 − 2x + 2
x0 xn+1 = g(xn) n ≥ 0
xn+1 = cos(xn) n ≥ 0
x0 ∈ R x0
8/17/2019 p01!12!2Soluciones de Ecuaciones No Lineales
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†
α
x = cos(x)
x + ln x = 0
α ≈ 0.5
F 1 : xn+1 = −
ln xn ; F 2 : xn+1 = e−xn ; F 3 : xn+1 =
xn + e−xn
2 .
† α
f
α ∈R
α
f /f
f (x) := (x − 1)(x − 2)2
f
f /f
x0
∈R f x = 2
f : R>0 → R f (x) = x + 1x − 2 {xn}n≥0
r = 1
f
xn+1 = 2 − 1xn
.
x0 > 1 {xn}n≥0 r = 1
{yn}n≥0 r = 1 f
{xn}n≥0
p(x) = x3 − x2 − x − 1
ξ ≈ 1.839 . . .
xn = g(xn−1)
g1(x) = (x + 1)2
x2 + 1 g2(x) = 1 +
1
x +
1
x2
g1(x) g2(x) ξ p(x)
g1(x) [1, 2] g2(x)
g1(x) x0 ≥ 0
M = E − e sin E
M
e
0 ≤ e
8/17/2019 p01!12!2Soluciones de Ecuaciones No Lineales
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g(E ) = M + e sin(E )
R g
M = 1
e = 0.5
g
E 0 ∈ [1, 2]
M e E 0
†
0.0167
M = 27/365 ∗ 2π
0 = E − e sin E − M
f : (a, b) →R
C2
(a, b)
α ∈ (a, b)
{xn}n≥0
x0
α
{xn}n≥0
xn+1 = xn − 2 f (xn)f (xn)
(n ≥ 0)
x0 α
x2 − x − 2 = 0
• g1(x) = x
2
− 2
• g2(x) = √ x + 2• g3(x) = 1 + 2x• g4(x) = x2+22x−1
2
|gi(2)|
†
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