Determine constants a-b-c such that iteration converges

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Reference no: EM13283480

Consider the fixed point iteration?
Xn+1= φ (xn), n=1,2,....
whereφ (x)=Ax+Bx2+Cx3
a) given appositive number α, determine the constants A,B,Csuch that the iteration converges locally to 1/α with orderp= 3. (this will give a cubically convergent method for computingthe reciprocal 1/α which uses on addition, subtraction, andmultiplication).
b) Determine a precise condition on the initial error ?o= xo - 1/α for iteration to converge

Reference no: EM13283480

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