Metodos de Interpolacion 2 DIAS PARA TRABAJAR

diferencia progresivas

Y (Δ)Y (Δ^2)Y (Δ^3)Y (Δ^4)Y (Δ^5)Y (Δ^6)YX= 0 85

-- -- 15X= 0.5 100 5

-- -- 20 -45X= 1 120 -40 -100

-- -- -20 55 -170X= 1.5 100 15 70 140

-- -- -5 -15 -30X= 2 95 0 40 -90

-- -- -5 25 -120X= 2.5 90 25 -80

-- -- 20 -55X= 3 110 -30

-- -- -10X= 3.5 100

-- --X= 7 0

-- --X= 8 0

-- --X= 9 0

-- --X= 10 0

Xi

𝑌_𝑘=𝑌_1+(𝑘¦1)∆𝑌_0+(𝑘¦2) ∆^2𝑌_0+…+(𝑘¦𝑗) ∆^𝑗 𝑌_0+(𝐾¦(𝑗+1))(0) (𝑘¦𝑗)=(𝐾¡)/((𝑘−𝑗)¡.𝐽¡)

(Δ^7)Y

-230

(𝑘¦𝑗)=(𝐾¡)/((𝑘−𝑗)¡.𝐽¡)

INTERPOLACION DE LAGRANGEPARA 6 DATOS

DATO PARA UN: X= 2.8

X F(X) X-X1 X-X2 X-X3 X-X4 X-X5X0 0 1.9 2.3 1.8 1.3 0.8 -0.2X1 0.5 2.39 -0.5 -1 -1.5 -2 -3X2 1 2.71 X0-X1 X0-X2 X0-X3 X0-X4 X0-X5X3 1.5 2.98X4 2 3.2 X-X0 X-X2 X-X3 X-X4 X-X5X5 3 2.98 2.8 1.8 1.3 0.8 -0.2

0.5 -0.5 -1 -1.5 -2.5X1-X0 X1-X2 X1-X3 X1-X4 X1-X5

X-X0 X-X1 X-X3 X1-X4 X1-X52.8 2.3 1.3 0.8 -0.2

1 0.5 -0.5 -1 -2X2-X0 X2-X1 X2-X3 X2-X4 X2-X5

X-X0 X-X1 X-X2 X-X4 X-X52.8 2.3 1.8 0.8 -0.21.5 1 0.5 -0.5 -1.5

X3-X0 X3-X1 X3-X2 X3-X4 X3-X5

X-X0 X-X1 X-X2 X-X3 X-X52.8 2.3 1.8 1.3 -0.2

2 1.5 1 0.5 -1X4-X0 X4-X1 X4-X2 X4-X3 X4-X5

X-X0 X-X1 X-X2 X-X3 X-X42.8 2.3 1.8 1.3 0.8

3 2.5 2 1.5 1X5-X0 X5-X1 X5-X2 X5-X3 X5-X4

PARA 5 DATOSDATO PARA UN:

X= 6

X F(X) X-X1 X-X2 X-X3 X-X4 F(Xo)X0 0 5 5 4 1 -1

5X1 1 7 -1 -2 -5 -7X2 2 9 X0-X1 X0-X2 X0-X3 X0-X4

X3 5 15X4 7 19 X-X0 X-X2 X-X3 X-X4 F(X1)

6 4 1 -171 -1 -4 -6

X1-X0 X1-X2 X1-X3 X1-X4

X-X0 X-X1 X-X3 X1-X4 F(X2)6 5 1 -1

92 1 -3 -5X2-X0 X2-X1 X2-X3 X2-X4

X-X0 X-X1 X-X2 X-X4 F(X3)6 5 4 -1

155 4 3 -2X3-X0 X3-X1 X3-X2 X3-X4

X-X0 X-X1 X-X2 X-X3 F(X4)6 5 4 1

197 6 5 2X4-X0 X4-X1 X4-X2 X4-X3

PARA 4 DATOSDATO PARA UN: X0 X1 X2 X3

X= 6 X 0 1 2 5F(X) 5 7 9 15

X-X1 X-X2 X-X3 F(Xo)5 4 1

5 =-1 -2 -5X0-X1 X0-X2 X0-X3

X-X0 X-X2 X-X3 F(X1)6 4 1

7 =1 -1 -4X1-X0 X1-X2 X1-X3

X-X0 X-X1 X-X3 F(X2)6 5 1

9 =2 1 -3X2-X0 X2-X1 X2-X3

X-X0 X-X1 X-X2 F(X3)6 5 4

15 =5 4 3

X3-X0 X3-X1 X3-X215


F(Xo) RESOLV. SOLUCION

1.9 = 0.363584F(X)= 3.1517747

F(X1) RESOLV.

2.39 = -2.67251712

F(X2) RESOLV.

2.71 = 7.2601984

F(X3) RESOLV.

2.98 = -9.8258944

F(X4) RESOLV.

3.2 = 6.429696

F(X5) RESOLV.

2.98 = 1.59670784

PARA 5 DATOS

RESOLV. SOLUCION

= -1.4285714286 F(X)= 17.00

RESOLV.

= 7

RESOLV.

= -9

RESOLV.

= 15

RESOLV.

= 5.4285714286

PARA 4 DATOS

RESOLV. SOLUCION

-10 F(X)= 17.00

RESOLV.

42

RESOLV.

-45

RESOLV.

30


DATO PARA UN: X= 2.8

X F(X) X-X1 X-X2 X-X3 X-X4X0 0 1.9 2.3 1.8 1.3 0.8X1 0.5 2.39 -0.5 -1 -1.5 -2X2 1 2.71 X0-X1 X0-X2 X0-X3 X0-X4X3 1.5 2.98X4 2 3.2 X-X0 X-X2 X-X3 X-X4X5 3 3.2 2.8 1.8 1.3 0.8X6 3.5 2.98 0.5 -0.5 -1 -1.5X7 4 2.74 X1-X0 X1-X2 X1-X3 X1-X4

X-X0 X-X1 X-X3 X-X42.8 2.3 1.3 0.8

1 0.5 -0.5 -1X2-X0 X2-X1 X2-X3 X2-X4

X-X0 X-X1 X-X2 X-X42.8 2.3 1.8 0.81.5 1 0.5 -0.5

X3-X0 X3-X1 X3-X2 X3-X4

X-X0 X-X1 X-X2 X-X32.8 2.3 1.8 1.3

2 1.5 1 0.5X4-X0 X4-X1 X4-X2 X4-X3

X-X0 X-X1 X-X2 X-X32.8 2.3 1.8 1.3

3 2.5 2 1.5X5-X0 X5-X1 X5-X2 X5-X3

X-X0 X-X1 X-X2 X-X3

2.8 2.3 1.8 1.33.5 3 2.5 2

X6-X0 X6-X1 X6-X2 X6-X3

X-X0 X-X1 X-X2 X-X32.8 2.3 1.8 1.3

4 3.5 3 2.5X7-X0 X7-X1 X7-X2 X7-X3

PARA 3 DATOSDATO PARA UN: X0 X1 X2

X= 6 X 0 1 2F(X) 5 7 9

X-X1 X-X2 F(Xo)5 4

5 =-1 -2X0-X1 X0-X2

X-X0 X-X2 F(X1)6 4

7 =1 -1X1-X0 X1-X2

X-X0 X-X1 F(X2)6 5

9=2 1

X2-X0 X2-X1


X-X5 X-6 X-X7 F(Xo) RESOLV.-0.2 -0.7 -1.2

1.9 = 0.0218150400-3 -3.5 -4X0-X5 X0-X6 X0-X7

X-X5 X-X6 X-X7 F(X1) RESOLV.-0.2 -0.7 -1.2

2.39 = -0.213801369600-2.5 -3 -3.5X1-X5 X1-X6 X1-X7

X-X5 X-X6 X-X7 F(X2) RESOLV.-0.2 -0.7 -1.2

2.71 = 0.813142220800-2 -2.5 -3X2-X5 X2-X6 X2-X7

X-X5 X-X6 X-X7 F(X3) RESOLV.-0.2 -0.7 -1.2

2.98 = -1.650750259200-1.5 -2 -2.5X3-X5 X3-X6 X3-X7

X-X5 X-X6 X-X7 F(X4) RESOLV.-0.2 -0.7 -1.2

3.2 = 1.80031488000-1 -1.5 -2X4-X5 X4-X6 X4-X7

X-X4 X-X6 X-X7 F(X5) RESOLV.0.8 -0.7 -1.2

3.2 = 2.880503808001 -0.5 -1X5-X4 X5-X6 X5-X7

X-X4 X-X5 X-X7 F(X6) RESOLV.

0.8 -0.2 -1.22.98 =

-0.4379541504001.5 0.5 -0.5X6-X4 X6-X5 X6-X7

X-X4 X-X5 X-X6 F(X7) RESOLV.0.8 -0.2 -0.7

2.74 = 0.0440434176002 1 0.5X7-X4 X7-X5 X7-X6

PARA 3 DATOS

RESOLV. SOLUCION

50 F(X)= 17.0000

RESOLV.

-168

RESOLV.

135

PARA 8 DATOS PARA 7 DATOSDATO PARA UN: X= 2.8

SOLUCION

F(X)= 3.25731358720

PARA 7 DATOSX0 X1 X2 X3 X4

X 0 0.5 1 1.5 2F(X) 1.9 2.39 2.71 2.98 3.2

X-X1 X-X2 X-X3 X-X4 X-X52.3 1.8 1.3 0.8 -0.2

-0.5 -1 -1.5 -2 -3X0-X1 X0-X2 X0-X3 X0-X4 X0-X5

X-X0 X-X2 X-X3 X-X4 X-X52.8 1.8 1.3 0.8 -0.20.5 -0.5 -1 -1.5 -2.5

X1-X0 X1-X2 X1-X3 X1-X4 X1-X5

X-X0 X-X1 X-X3 X1-X4 X1-X52.8 2.3 1.3 0.8 -0.2

1 0.5 -0.5 -1 -2X2-X0 X2-X1 X2-X3 X2-X4 X2-X5

X-X0 X-X1 X-X2 X-X4 X-X52.8 2.3 1.8 0.8 -0.21.5 1 0.5 -0.5 -1.5

X3-X0 X3-X1 X3-X2 X3-X4 X3-X5

X-X0 X-X1 X-X2 X-X3 X-X52.8 2.3 1.8 1.3 -0.2

2 1.5 1 0.5 -1X4-X0 X4-X1 X4-X2 X4-X3 X4-X5

X-X0 X-X1 X-X2 X-X3 X-X42.8 2.3 1.8 1.3 0.8

3 2.5 2 1.5 1X5-X0 X5-X1 X5-X2 X5-X3 X5-X4

X-X0 X-X1 X-X2 X-X3 X-X42.8 2.3 1.8 1.3 0.83.5 3 2.5 2 1.5

X6-X0 X6-X1 X6-X2 X6-X3 X6-X4

PARA 7 DATOSX5 X6

3 3.53.2 2.98

SOLUCION

F(X)= 3.261385728000X-X6 F(Xo) RESOLV.

-0.71.9 = 0.0727168-3.5

X0-X6

X-X6 F(X1) RESOLV.-0.7

2.39 = -0.623587328000001-3X1-X6

X1-X6 F(X2) RESOLV.-0.7

2.71 = 2.032855552-2.5X2-X6


2.98 = -3.43906304-2X3-X6


3.2 = 3.0005248-1.5X4-X6


3.2 =2.40041984-0.5

X5-X6


2.98 = -0.1824808960000.5X6-X5

PARA 7 DATOS PARA 9 DATOSDATO PARA UN: X= 2.8

X F(X) X-X1 X-X2X0 0 1.9 2.3 1.8X1 0.5 2.39 -0.5 -1X2 1 2.71 X0-X1 X0-X2X3 1.5 2.98X4 2 3.2 X-X0 X-X2X5 3 3.2 2.8 1.8X6 3.5 2.98 0.5 -0.5X7 4 2.74 X1-X0 X1-X2X8 5 2.64

X-X0 X-X12.8 2.3

1 0.5X2-X0 X2-X1

X-X0 X-X12.8 2.31.5 1

X3-X0 X3-X1

X-X0 X-X12.8 2.3

2 1.5X4-X0 X4-X1

X-X0 X-X12.8 2.3

3 2.5X5-X0 X5-X1

X-X0 X-X1

2.8 2.33.5 3

X6-X0 X6-X1

X-X0 X-X12.8 2.3

4 3.5X7-X0 X7-X1

X-X0 X-X12.8 2.3

5 4.5X8-X0 X8-X1

PARA 9 DATOS

X-X3 X-X4 X-X5 X-6 X-X7 X-X8 F(Xo)1.3 0.8 -0.2 -0.7 -1.2 -2.2

1.9 =-1.5 -2 -3 -3.5 -4 -5X0-X3 X0-X4 X0-X5 X0-X6 X0-X7 X0-X8

X-X3 X-X4 X-X5 X-X6 X-X7 X-X8 F(X1)1.3 0.8 -0.2 -0.7 -1.2 -2.2

2.39 =-1 -1.5 -2.5 -3 -3.5 -4.5X1-X3 X1-X4 X1-X5 X1-X6 X1-X7 X1-X8

X-X3 X-X4 X-X5 X-X6 X-X7 X-X8 F(X2) =1.3 0.8 -0.2 -0.7 -1.2 -2.22.71-0.5 -1 -2 -2.5 -3 -4

X2-X3 X2-X4 X2-X5 X2-X6 X2-X7 X2-X8

X-X2 X-X4 X-X5 X-X6 X-X7 X-X8 F(X3)1.8 0.8 -0.2 -0.7 -1.2 -2.2

2.98 =0.5 -0.5 -1.5 -2 -2.5 -3.5X3-X2 X3-X4 X3-X5 X3-X6 X3-X7 X3-X8

X-X2 X-X3 X-X5 X-X6 X-X7 X-X8 F(X4)1.8 1.3 -0.2 -0.7 -1.2 -2.2

3.2 =1 0.5 -1 -1.5 -2 -3X4-X2 X4-X3 X4-X5 X4-X6 X4-X7 X4-X8

X-X2 X-X3 X-X4 X-X6 X-X7 X-X8 F(X5)1.8 1.3 0.8 -0.7 -1.2 -2.2

3.2 =2 1.5 1 -0.5 -1 -2X5-X2 X5-X3 X5-X4 X5-X6 X5-X7 X5-X8

X-X2 X-X3 X-X4 X-X5 X-X7 X-X8 F(X6)

1.8 1.3 0.8 -0.2 -1.2 -2.22.98 =

2.5 2 1.5 0.5 -0.5 -1.5X6-X2 X6-X3 X6-X4 X6-X5 X6-X7 X6-X8

X-X2 X-X3 X-X4 X-X5 X-X6 X-X8 F(X7)1.8 1.3 0.8 -0.2 -0.7 -2.2

2.74 =3 2.5 2 1 0.5 -1X7-X2 X7-X3 X7-X4 X7-X5 X7-X6 X7-X8

X-X2 X-X3 X-X4 X-X5 X-X6 X-X7 F(X8)1.8 1.3 0.8 -0.2 -0.7 -1.2

2.64 =4 3.5 3 2 1.5 1X8-X2 X8-X3 X8-X4 X8-X5 X8-X6 X8-X7

PARA 9 DATOS

RESOLV. SOLUCION

0.0218150400F(X)= 3.25888529066667

RESOLV.

-0.213801369600

RESOLV.

0.813142220800

RESOLV.

-1.650750259200

RESOLV.

1.80031488000

RESOLV.

2.88050380800

RESOLV.

-0.437954150400

RESOLV.

0.044043417600

RESOLV.

0.001571703467

INTERPOLACIÓN INVERSA

PARA 9 DATOSDATO PARA UN:f(X) 2.8

X F(X) f(X)-f(X2) f(X)-f(X3)X1 0.2 -1.472 3.456 2.304X2 0.4 -0.656 -0.816 -1.968X3 0.6 0.496 f(X1)-f(X2) f(X1)-f(X3)X4X5 f(X)-f(X1) f(X)-f(X3)X6 4.272 2.304X7 0.816 -1.152X8 f(X2)-f(X1) f(X2)-f(X3)X9

f(X)-f(X1) f(X)-f(X2)2.6 2.4

1.968 1.152f(X3)-f(X1) f(X3)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X4)-f(X1) f(X4)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X5)-f(X1) f(X5)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X6)-f(X1) f(X6)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X7)-f(X1) f(X7)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X8)-f(X1) f(X8)-f(X2)

f(X)-f(X1) f(X)-f(X2)4.272 3.4561.472 0.656

f(X9)-f(X1) f(X9)-f(X2)


PARA 9 DATOS

f(X)-f(X4) f(X)-f(X5) f(X)-f(X6) f(X)-f(X7) f(X)-f(X8) f(X)-f(X9)2.8 2.8 2.8 2.8 2.8 2.8

-1.472 -1.472 -1.472 -1.472 -1.472 -1.472f(X1)-f(X4) f(X1)-f(X5) f(X1)-f(X6) f(X1)-f(X7) f(X1)-f(X8) f(X1)-f(X9)


-0.656 -0.656 -0.656 -0.656 -0.656 -0.656f(X2)-f(X4) f(X2)-f(X5) f(X2)-f(X6) f(X2)-f(X7) f(X2)-f(X8) f(X2)-f(X9)


0.496 0.496 0.496 0.496 0.496 0.496f(X3)-f(X4) f(X3)-f(X5) f(X3)-f(X6) f(X3)-f(X7) f(X3)-f(X8) f(X3)-f(X9)


-0.496 0 0 0 0 0f(X4)-f(X3) f(X4)-f(X5) f(X4)-f(X6) f(X4)-f(X7) f(X4)-f(X8) f(X4)-f(X9)










PARA 9 DATOS

X1 RESOLV. SOLUCION

-1.472 = -7.2987546628F(X)= 0.93512737127371

X2 RESOLV.

-0.656 = 6.8687058824

X3 = RESOLV.

0.496 1.3651761518

X4 RESOLV.

0 = #DIV/0!

X5 RESOLV.

0 = #DIV/0!

X6 RESOLV.

0 = #DIV/0!

X7 RESOLV.

0 = #DIV/0!

X8 RESOLV.

0 = #DIV/0!

X9 RESOLV.

0 = #DIV/0!


PARA 9 DATOS

INTERPOLACION ITERADA O NEVILLEencontrar el valor de x usando el metodo de Nevillei 0 1 2 3 4 5x 1 1.3 1.6 1.9 2.2f(x) 0.7651987 0.620086 0.4554022 0.2818186 0.1103623

Q 0,0 Q 1,0 Q 2,0 Q 3,0 Q 4,0 Q 5,0

INTERPOLACION ITERADA O NEVILLEencontrar el valor de x usando el metodo de Neville X = 1.5

6 7 8 9

i X Q f(x)

0 1 0.7651987

1 1.3 0.620086

2 1.6 0.4554022

3 1.9 0.2818186

4 2.2 0.1103623

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

Q 6,0 Q 7,0 Q 8,0 Q 9,0

Q 0,0

Q 1,1

Q 1,0

Q 2,1

Q 2,0

Q 3,1

Q 3,0

Q 4,1

Q 4,0

Q 5,1

Q 5,0

Q 6,1

Q 6,0

Q 7,1

Q 7,0

Q 8,1

Q 8,0

Q 9,1

Q 9,0

𝑸(𝒊,𝒋) (𝒙)=[(𝑿−𝑿(𝒊−𝒋) )𝑸(𝒊 , 𝒋−𝟏)−(𝑿−𝑿𝒊)𝑸(𝒊−𝟏 , 𝒋−𝟏) ]/(𝑿𝒊−𝑿(𝒊−𝒋) )

INTERPOLACION ITERADA O NEVILLE

0.5233442

0.51247137

0.5102968 0.51181264

0.51128567 0.51181997

0.5132634 0.51183021 0.51150507

0.51373613 0.51244975

0.510427 0.50780326 #DIV/0!

0.41881016 #DIV/0!

0.07524702 #DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0!

#DIV/0!

Q 2,2

Q 3,3

Q 3,2 Q 4,4

Q 4,3 Q 5,5

Q 4,2 Q 5,4

Q 5,3 Q 6,5

Q 5,2 Q 6,4

Q 6,3 Q 7,5

Q 6,2 Q 7,4

Q 7,3 Q 8,5

Q 7,2 Q 8,4

Q 8,3 Q 9,5

Q 8,2 Q 9,4

Q 9,3

Q 9,2


Q11

Q1,1 = [(X-Xo)Q1,0 - (X-X1)Qo,o] / X1-Xo

Q13

Q2,1 = [(X-X1)Q2,o - (X-X2)Q1,o] / X2-X1

Q15

Autor:

Q17

Q4,1 = [(X-X3)Q4,o - (X-X4)Q3,o] / X4-X3

Q19

Q1,1 = [(X-X4)Q5,0 - (X-X5)Q4,o] / X5-Xo

Q21

Q6,1 = [(X-X5)Q6,0 - (X-X6)Q5,o] / X6-X5

#DIV/0!

#DIV/0!

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0! #DIV/0!

#DIV/0!

#DIV/0!

Q 6,6

Q 7,7

Q 7,6 Q 8,8

Q 8,7 Q 9,9

Q 8,6 Q 9,8

Q 9,7

Q 9,6


DIFERENCIA DIVIDIDASencontrar el valor de x usando el metodo de Neville

i 0 1 2 3 4 5 6x -1 -0.96 -0.86 -0.79 0.22 0.5 0.936

f(x) -1 -0.151 0.894 0.986 0.895 0.5 -0.306

0 Dif. 1 Dif. 2 Dif 3 Dif 4 Dif.i X0 -1 -1

21.2251 -0.96 -0.151 -76.96428571

10.45 110.5942376950772 -0.86 0.894 -53.7394958 -54.22482697

1.314285714 44.43994879001743 -0.79 0.986 -1.300356226 -30.2990063

-0.09009901 0.203399598640084 0.22 0.895 -1.023732772 0.019697281

-1.410714286 0.23877591584695 0.5 0.5 -0.611605541 13.68967382

-1.848623853 11.05361823354246 0.936 -0.306 -3.043401553 #DIV/0!

-0.326923077 #DIV/0!7 0 0 #DIV/0! #DIV/0!

#DIV/0! #DIV/0!8 0 0 #DIV/0! #DIV/0!

#DIV/0! #DIV/0!9 0 0 #DIV/0!

#DIV/0!10 0 0

Determinar el polinomio de 1er,2do,3er,4to…. 10mo grado

Polinomio de 1er grado Polinomio de 2do grado

Polinomio de 4to grado

f(Xi) f(Xi,Xi+1) f(Xi,Xi+1,Xi+2) f(Xi,Xi+1,Xi+2,Xi+3) f(Xi,...,Xi+4)

P(x)=f(Xo)+(X-Xo)f[Xo,X1] P(x)=f(Xo)+(X-Xo)f[Xo,X1]+(X-Xo)(X-X1)f[Xo,X1,X2]

P(x)=f(Xo)+(X-Xo)f[Xo,X1]+(X-Xo)(X-X1)f[Xo,X1,X2]+(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]+(X-X0)(X-X1)(X-X2)(X-X3)f[Xo,X1,X2,X3,X4]

DIFERENCIA DIVIDIDASencontrar el valor de x usando el metodo de Neville

7 8 9 10

5 Dif. 6 Dif. 7 Dif. 8 Dif. 9 Dif. 10 Dif.

15.950547120.020831765

15.99087741 -0.12036912-0.09953735 #DIV/0!

15.89532156 #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0!

#DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0!

#DIV/0! #DIV/0!#DIV/0!

#DIV/0!

Determinar el polinomio de 1er,2do,3er,4to…. 10mo grado

Polinomio de 2do grado Polinomio de 3er grado

Polinomio de 4to grado Polinomio de 4to grado

f(Xi,...,Xi+5) f(Xi,...,Xi+6) f(Xi,...,Xi+7) f(Xi,...,Xi+8) f(Xi,...,Xi+9) f(Xi,...,Xi+10)

(X-Xo)(X-X1)f[Xo,X1,X2] P(x)=f(Xo)+(X-Xo)f[Xo,X1]+(X-Xo)(X-X1)f[Xo,X1,X2]+(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]

(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]+(X-X0)(X-X1)(X-X2)(X-X3)f[Xo,X1,X2,X3,X4] P(x)=f(Xo)+(X-Xo)f[Xo,X1]+(X-Xo)(X-X1)f[Xo,X1,X2]+(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]+(X-X0)(X-X1)(X-X2)(X-X3)f[Xo,X1,X2,X3,X4]+(X-Xo)(X-X1)(X-X2)(X-X3)(X-X4)f[Xo,X1,X2,X3,X4,X5]

DIFERENCIA DIVIDIDAS

Polinomio de 3er grado

Polinomio de 4to grado

(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]

(X-Xo)(X-X1)f[Xo,X1,X2]+(X-Xo)(X-X1)(X-X2)f[Xo,X1,X2,X3]+(X-X0)(X-X1)(X-X2)(X-X3)f[Xo,X1,X2,X3,X4]+(X-Xo)(X-X1)(X-X2)(X-X3)(X-X4)f[Xo,X1,X2,X3,X4,X5]

MINIMOS CUADRADOS

Inserta: N= 5rN° X^2 X*Y

1 0 0.12 0 02 2 0.153 4 0.3063 3 0.17 9 0.514 6 0.225 36 1.355 7 0.26 49 1.826 0 07 0 08 0 09 0 0

10 0 0∑(X)= 18 ∑(Y)= 0.928 ∑(X^2)= 98 ∑(X*Y)=

0.115639 0.0194337

Y= 0.11564 + 0.0194337 X

MINIMOS CUADRADOS SEGUNDO GRADO

N = 5

N° X^2 X^31 -2 0 4 -82 -1 0 1 -13 0 1 0 04 1 1 1 15 2 3 4 86 0 07 0 08 0 09 0 0

Xi Yi

a0= a1=

Xi Yi

1er grado𝒂O=[(∑𝒚)(∑𝒙^𝟐 )−(∑𝒙)(∑𝒙𝒚)] / [𝑵*∑𝒙^𝟐−(∑𝒙)^𝟐 ]

𝒀=+𝒂_𝟎+𝒂𝟏 𝐗+𝒂_𝟐 𝑿^𝟐

10 0 011 0 0

∑(X)= 0 ∑(X)= 5 ∑(X)= 10 ∑(X)=

Resultado : Sistema de ecuaciones.

1.- 5 + 0

2.- 0 + 10

3.- 10 + 0

MINIMOS CUADRADOS DE TERCER GRADO

N = 6

N° X^2 X^31 280 280 78400 219520002 650 650 422500 2746250003 1000 1000 1000000 10000000004 1200 1200 1440000 17280000005 1500 1500 2250000 33750000006 1700 1700 2890000 49130000007 0 08 0 09 0 0

10 0 011 0 0

∑(X)= 6330 ∑(X)= 6330 ∑(X)= 8080900 ∑(X)=


1.- 6 + 6330

2.- 6330 + 8080900

3.- 8080900 + 1.1313E+10

4.- 1.131E+10 + 1.6673E+13

a0 a1

a0 a1

a0 a1

Xi Yi

a0 a1

a0 a1

a0 a1

a0 a1

N = 6

N° X^2 X^31 1 25 1 12 2 34 4 83 3 42 9 274 4 58 16 645 5 60 25 1256 6 62 36 2167 7 65 49 3438 8 63 64 5129 9 67 81 729

10 0 011 0 0

∑(X)= 45 ∑(X)= 476 ∑(X)= 285 ∑(X)=


1.- 6 + 45

2.- 45 + 285

3.- 285 + 2025

4.- 2025 + 15333

Xi Yi

a0 a1

a0 a1

a0 a1

a0 a1

MINIMOS CUADRADOS

X*Y0

0.3060.511.351.82

00000

3.986

MINIMOS CUADRADOS SEGUNDO GRADO

X^3 X^4 X*Y (X^2)*Y-8 16 0 0-1 1 0 00 0 0 01 1 1 18 16 6 120 0 0 00 0 0 00 0 0 00 0 0 0

1er grado𝒂O=[(∑𝒚)(∑𝒙^𝟐 )−(∑𝒙)(∑𝒙𝒚)] / [𝑵*∑𝒙^𝟐−(∑𝒙)^𝟐 ] 𝒂1=[𝑵*∑𝒙𝒚−(∑𝒙)(∑𝒚)] / [𝑵*∑𝒙^𝟐−(∑𝒙)^𝟐 ]

𝒀=+𝒂_𝟎+𝒂𝟏 𝐗+𝒂_𝟐 𝑿^𝟐

0 0 0 00 0 0 0

0 ∑(X)= 34 ∑(X)= 7 ∑(X)= 13

+ 10 = 5

+ 0 = 7

+ 34 = 13

MINIMOS CUADRADOS DE TERCER GRADO

X^3 X^4 X^5 X^6 X*Y21952000 6146560000 1721036800000 481890304000000 78400

274625000 178506250000 116029062500000 7.5418890625E+016 4225001000000000 1000000000000 1000000000000000 1E+018 10000001728000000 2073600000000 2488320000000000 2.985984E+018 14400003375000000 5062500000000 7593750000000000 1.1390625E+019 22500004913000000 8352100000000 1.419857E+016 2.4137569E+019 2890000

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

1.131E+10 ∑(X)= 1.6673E+13 ∑(X)= 2.5398E+16 ∑(X)= 3.959E+19 ∑(X)=

+ 8080900 + a3 1.1313E+10 = 6330

+ 1.1313E+10 + a3 1.6673E+13 = 8080900

+ 1.6673E+13 + a3 2.5398E+16 = 1.1313E+10

+ 2.5398E+16 + a3 3.959E+19 = 1.6673E+13

a2

Calcular con calculadora: CASIO FX "2.0 PLUSa2

a2

a2

a2

a2

a2

X^3 X^4 X^5 X^6 X^71 1 1 1 18 16 32 64 128

27 81 243 729 218764 256 1024 4096 16384

125 625 3125 15625 78125216 1296 7776 46656 279936343 2401 16807 117649 823543512 4096 32768 262144 2097152729 6561 59049 531441 4782969

0 0 0 0 00 0 0 0 0

2025 ∑(X)= 15333 ∑(X)= 120825 ∑(X)= 978405 ∑(X)=

+ 285 + a3 2025 + a4

+ 2025 + a3 15333 + a4

+ 15333 + a3 120825 + a4

+ 120825 + a3 978405 + a4

a2

a2

a2

a2

MINIMOS CUADRADOS

𝒂1=[𝑵*∑𝒙𝒚−(∑𝒙)(∑𝒚)] / [𝑵*∑𝒙^𝟐−(∑𝒙)^𝟐 ]

X*Y (X^2)*Y (X^3)*Y78400 21952000 6146560000

422500 274625000 1785062500001000000 1000000000 10000000000001440000 1728000000 20736000000002250000 3375000000 50625000000002890000 4913000000 8352100000000

0 0 00 0 00 0 00 0 00 0 0

8080900 ∑(X)= 1.1313E+10 ∑(X)= 1.6673E+13

Calcular con calculadora: CASIO FX "2.0 PLUS

X^7 X^8 X*Y (X^2)*Y (X^3)*Y1 1 25 25 25

128 256 68 136 2722187 6561 126 378 1134

16384 65536 232 928 371278125 390625 300 1500 7500

279936 1679616 372 2232 13392823543 5764801 455 3185 22295

2097152 16777216 504 4032 322564782969 43046721 603 5427 48843

0 0 0 0 00 0 0 0 0

8080425 ∑(X)= 67731333 ∑(X)= 2685 ∑(X)= 17843 ∑(X)=

15333 =

120825 =

978405 =

8080425 =

Calcular con calculadora: CASIO FX "2.0 PLUS

(X^3)*Y x^9 x^10 x^11 x^1225 1 1 1 1

272 512 1024 2048 40961134 19683 59049 177147 5314413712 262144 1048576 4194304 167772167500 1953125 9765625 48828125 244140625

13392 10077696 60466176 362797056 217678233622295 40353607 282475249 1977326743 1384128720132256 134217728 1073741824 8589934592 6871947673648843 387420489 3486784401 31381059609 282429536481.00

0 574304985 4914341925 42364319625 367428536133.000

129429

(x^4)*y (x^5)*y (x^6)*y25 25 25

544 1088 21763402 10206 30618

14848 59392 23756837500 187500 93750080352 482112 2892672

156065 1092455 7647185258048 2064384 16515072439587 3956283 35606547990371 7853445 63869363

a= 0 n=

b = 3 h =(a-b)/n=n X f(x)0 0.0001 0.3002 0.6003 0.9004 1.2005 1.5006 1.8007 2.1008 2.4009 2.700

10 3.000

10

0.3

REGLA DE SIMPSON

simpson 1/3 Simple

a x1 b f(xo) f(x1) f(x2) Intg analitica0 0.4 0.8 0.2 2.456 0.232 1.640533

simpson 1/3 multipleb 2 na 0 integ analitich 0.25 Fmedia''''

X f(X)0 0 suma impar suma par I

0.625 0.18324077 0.73022503 0.62844884 0.351879690.875 0.245583021.125 0.264295291.375 0.243269921.625 0.196333711.875 0.139595912.125 0.086355262.375 0.04475847

simpson 3/8b 2 na 0 integ analitich 0.66666667 fmedia ''''

X f(x)0 0.2 I Et Et%

0.66666667 2.87489712 854.103704 -852.463171 51962.57381.33333333 119.130041

2 3050.2

C5

para puntos impares o espacios pares

H9

Integral Analitica de la funcion

F22

modificar posicion impar

G22

modificar posicion par

H22

modificar ultima posicion

C35

espacios impares, o puntos pares

REGLA DE SIMPSON

I Et Et% fmedia'''' Ea1.36746667 0.27306633 16.6449766 -2400 0.27306667

81.640533

-2400

et et% Ea1.28865331 78.5508924 0.10416667

I total 854.455583Error -852.81505e % 51984.0229

31.640533

-2400

Ea11.8518519

L9

Integral de la cuarta derivada entre b-a

L30

por si piden conbinar

Metodos de Interpolacion 2 DIAS PARA TRABAJAR

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