mathcad_interpolacao_vandermond

Exercício da Página 2 do Capítulo 3: implementar no MATHCAD a interpolação da função: senh( ) ( ) sen h( ) x y f x x Φ = = Φ TOL 10 9 − := Φ 5 := c sinh Φ ( ) := f x ( ) y Φ c ← x 0 = if y sinh Φ x ⋅ ( ) x c ⋅ ← otherwise y := Coef ∆x ( ) n .8 ∆x ← x .1 i ∆x ⋅ + ← pot 1 ← b i f x ( ) ← A i j , pot ← pot pot x ⋅ ← j 0 n .. ∈ for i 0 n .. ∈ for c lsolve A b , ( ) ← c := p int x c , ( ) n last c ( ) ← y c n ← y y x ⋅ c i + ← i n 1 − 0 .. ∈ for y := ∆x .04 := c Coef ∆x ( ) := f int x ( ) p int x c , ( ) := k 0 100 .. := x k k 100 := 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 f x k ( ) f int x k ( ) x k Comparação entre a função e sua forma interpolada ∆x 0.04 = 0 0.2 0.4 0.6 0.8 1 0 2 10 11 − × 4 10 11 − × 6 10 11 − × 8 10 11 − × f x k ( ) f int x k ( ) − x k Erro da Interpolação Polinomial

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Exerccio da Pgina 2 do Captulo 3: implementar no MATHCAD a interpolao da funo:

senh( )( )senh( )

xy f xx

= =

TOL 10 9:= 5:= c sinh ( ):= f x( ) y c

x 0=if

ysinh x( )

x c otherwise

y

:=

Coef x( ) n.8x

x .1 i x+pot 1bi f x( )

Ai j, potpot pot x

j 0 n..for

i 0 n..for

c lsolve A b, ( )c

:=

pint x c, ( ) n last c( )y cn

y y x ci+i n 1 0..for

y

:=

x .04:= c Coef x( ):= fint x( ) pint x c, ( ):=k 0 100..:= xk

k100

:=

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

f xk( )fint xk( )

xk

Comparao entre a funo e sua forma interpolada

x 0.04=

0 0.2 0.4 0.6 0.8 10

2 10 114 10 116 10 118 10 11

f xk( ) fint xk( )

xk

Erro da Interpolao Polinomial