Interpolacion

CONJUNTO DE EJERCICIOS 3.1
3-
C) f(0.25) si f(0.1) = 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4)= 0.24842440

1
| X1 | F(x1) |
X0 | 0.2 | -0.28398668 |
X1 | 0.3 |0.00660095 |
x | 0.25 | |

f(x) x-x1x0-x1 f(x) + x-x1x0-x1 f(x1)
(0.25-0.3)(0.2-0.3) f(-0.28398668) + (0.25-0.3)(0.2-0.3)f(0.00660095)=
f(x) = - 0.14199334 + 3.300475x10-03f(x)= 0.13869287
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2

| X1 | F(x1) |
X0 | | |
X1 | | |
X2 | | |
x | | |F2(x)= x-x1(x-x2)(x0-x1)(x0-x2) f(x0) + (x-x0)(x-x2)(x1-x0)(x1-x2) f(x1) + (x-x0)(x-x1)x2-x0x2-x1 f(x2)

F2(x)= ()()() f() + ()()()() f() + ()() f() =
F(x)= () +() + () =-------------------------------------------------------------------------------------------------------
3
| xi | F(xi) |
x0 | | |
x1 | | |
x2 | | |
x3 | | |

F3(x)=x-x1(x-x2)(x-x3)(x0-x1)(x0-x2)(x0-x3) f(x0) + (x-x0)(x-x2)(x-x3)(x1-x0)(x1-x2)(x1-x3) f(x1) +
(x-x0)(x-x1)(x-x3)x2-x0x2-x1(x2-x3) f(x2) + (x-x0)(x-x1)(x-x2)(x3-x0)(x3-x1)(x3-x2) f(x3)

F3(x)= ()()()()() f() + ()()()()()()f() + ()()()() f() + ()()()()()() f()=
f(x) = () + () + () + () =


1
d) F(0.9) si f(0.6) = -017694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) = 0.65809197

| X1 | F(x1)|
X0 | 0.8 | 0.22363362 |
X1 | 1.0 | 0.65809197 |
x | 0.9 | |

1- f(x) x-x1x0-x1 f(x) + x-x1x0-x1 f(x1)

f(x) = (0.9-1.0)(0.8-1.0) f(0.22363362) +(0.9-1.0)(0.8-1.0)f(0.65809197)=

f(x) = 0.1118168 + 0.3290460 = 0.4408628
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2

| X1 | F(x1) |
X0 | 0.8 |0.22363362 |
X1 | 1.0 | 0.65809197 |
X2 | 0.7 | 0.0137227 |
x | 0.9 | |

F2(x)= x-x1(x-x2)(x0-x1)(x0-x2) f(x0) + (x-x0)(x-x2)(x1-x0)(x1-x2) f(x1) + (x-x0)(x-x1)x2-x0x2-x1 f(x2)

F2(x) =...