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Método de Lagrange:

Pn(x)=b0(x-x1)(x-x2)...(x-xn)+...+bn(x-x0)(x-x1)...(x-xn-1)

Xn Yn

3 -7 b0 0.38888889 0,000 (x-3) (x-0)(x-6)(x

0 -2 b1 0.11111111 0,000 (x-0) (x-3)(x-6)(x

6 3 b2 0.03333333 0,000 (x-6) (x-3)(x-0)(x1 4 b3 0.4 0,000 (x-1) (x-3)(x-0)(x

Solución: P(x)=0,000(x-0)(x-6)(x-1)+0,000(x-3)(x-6)(x-1)+0,000(x-3)(x-0)(x-1)+0,000(x-3)(x-0

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Xn Yn

2 0.4666666667

3.' -10.4'833333

6.1 '.3'66

1.001 4.00029'2343

bi=  y

i

( xi− x

0)( x

i− x

1)⋅⋯⋅( x

i− x

i−1)( xi− x

i+1 )⋅

7/21/2019 Poli No Mio Lagrange

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-1)

-1)

-1)-6)

(x-6)

 yi

i− x

1)⋅⋯⋅( x

i− x

i−1 )( x i− x

i+1 )⋅⋯⋅( xi− x

n)

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Método de Lagrange:

Pn(x)=b0(x-x1)(x-x2)...(x-xn)+...+bn(x-x0)(x-x1)...(x-xn-1)

Xn Yn

8 0.0236 b0 0.00006

10 0.047' b1 -0.00049

12 0.083 b2 0.0013014 0.1736 b3 -0.00181

16 0.202 b4 0.000'3

Solución: P4(x)= 0,00006(x-10)(x-12)(x-14)(x-16)-0,00049(x-8)(x-12)(x-14)(x-16)+0,00130

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Xn Yn

7 -0.041'62'

9 0.0431

8.' 0.03691211

bi=  y

i

( xi− x

0)( x

i− x

1)⋅⋯⋅( x

i− x

i−1)( x i− x

i+1)⋅⋯⋅(

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x-8)(x-10)(x-14)(x-16)-0,00181(x-8)(x-10)(x-12)(x-16)+0,000'3(x-8)(x-10)(x-12)(x-14)

 yi

⋅⋯⋅( xi− x

i−1 )( x i− x

i+1)⋅⋯⋅( xi− x

n)