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[SPAM] [obm-l] Métodos Numéricos - Teoria dos Erros
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- Subject: [SPAM] [obm-l] Métodos Numéricos - Teoria dos Erros
- From: "Daniel S. Braz" <dsbraz@xxxxxxxxx>
- Date: Thu, 10 Apr 2008 01:02:45 -0300
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Senhores,
(Desculpem a insistência, sei que já envie este problema à lista,porém não obtive resposta)
Por favor, alguém pode me ajudar a entender este problema?
Seja um sistema de aritmética de ponto flutuante de quatro dígitos,base decimal e com acumulador de precisão dupla. Dados os números:
x = 0,7237*10^4y = 0,2145*10^-3z = 0,2585*10^1
efetue as seguintes operações e obtenha o erro relativo no resultado,supondo que x, y e z estão exatamente representados:
x + y + z
= (0,7237 + 0,00000002)*10^4 + 0,0002585*10^4
= (0,72370002 + 0,0002585)*10^4
= 0,72395852*10^4 ---> 0,7240*10^4 #
E_x = 0 ; E_y = 0,0725 ; E_z = 0
E_(x+y) = 0 + 0,0725[(0,00000002*10^4)/(0,72370002*10^4)] + E_1 ;|E_1| < 0,5*10^-3
= 0 + 2*10^-9 + E_1
= E_1
E_[(x+y)+z)] = E_1[(0,72370002*10^4)/(0,72395852*10^4)] + 0 + E_2 ;|E_2| < 0,5*10^-3
= 0,99964293*E_1 + E_2
|E_[(x+y)+z)]| < 0,99964293*|E_1| + |E_2| ; |E_1| = |E_2| = 0,5*10^-3
< 0,99982146*10^-3 ---> 0,9998*10^-3 #
No livro a responsta é: |E_[(x+y)+z)]| < 10^-3
Obrigado.
Daniel.
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