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Problem: Birge-Vieta method x^4-3x^3+3x^2-3x+2, p=0.5 [ Calculator, Method and examples ]

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Your problem -> Birge-Vieta method x^4-3x^3+3x^2-3x+2, p=0.5

 x^4-3x^3+3x^2-3x+2=0

In this problem the coefficients are a_0=1,a_1=-3,a_2=3,a_3=-3,a_4=2

Let the initial approximation to p be p_0=0.5

1^(st) iteration :

 p_00.5 a_01 a_1-3 a_23 a_3-3 a_42 p_0*b_00.5 p_0*b_1-1.25 p_0*b_20.875 p_0*b_3-1.0625 b_01 b_1=a_1+p_0*b_0-2.5 b_2=a_2+p_0*b_11.75 b_3=a_3+p_0*b_2-2.125 b_4=a_4+p_0*b_30.9375 p_0*c_00.5 p_0*c_1-1 p_0*c_20.375 c_01 c_1=b_1+p_0*c_0-2 c_2=b_2+p_0*c_10.75 c_3=b_3+p_0*c_2-1.75

p_1=p_0-b_4/c_3=0.5-(0.9375)/(-1.75)=1.0357

2^(nd) iteration :

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