Numerical Analysis & it’s applications Q4 only part (ii) of the question needs answering. Part (i) is answered and the answer is included here. Thanks. 4. (Fired-Point Iteration Method;Consider the problem of finding the root of the polynomialf (x) = x* - 0.89x - 1.08in [1, 2].(i) Show thatf (x)f'(x)f(x) = 0 = x = x -on [1, 2], thereby reducing the root-finding problem to the fixed-point problem for the functionf(x)f'(x)g(x) = x -on [1,2].(ii) Use the Fixed-Point Iteration method to find an approximation pN of the fixed-point p of g(x) in [1, 2], the root of the polynomial f(x) in[1, 2], satisfying RE(pN PN-1) < 10-6 by taking po = 1 as the initial approximation. All calculations are to be carried out in the FPA7. Presentthe results of your calculations in a standard output table for the method of the formPn-1Pn RE(pn = Pn-1) Step1a)let un eapressStep3c)fen=o s ax approximale fro byeguahin win Ihe neghbourhood offorat degre e equahan.(0.89*1.06)"s中ca)prh degureIheIherimaywrilefrm= aox+ a, = 6-0Step2Ashere a.t0. and a, ave arbihompavamelas. a beappropnale Cnditansdelnmınid by preseribedon f ) and ils denvaluisb)tiwoocx ) = (os9x + os )on Substiluting ao and a, from O sin and represtentinghi approximalue volues a x by xes ocueobtain%3DFrax)he problem of tinding rat of he eg Ois egenvaledat lhe point (**itx) wilk IhiTheevaluahen'. fe, te' each eleration(o-59)letX0=1+2=1-5Lwid'ns) =Repsomilhd reuirgNewtonSuppore x* s the exact8olution for= 0At he 4 N-R. ite vaten,defne lhe erm (Ei:whuch es dhaving cğuadrahcConvergina - EurCCEE, cs Canalointfro is molle and f'ram)foand 1x-x* |l fmook endughYsdoal Comurrgence%3D0-2391く1%3D=1-2466, (a ): Co$9+ 1-08)""= (6 89 C1·2u6o)t 18)"-2164$3c*)= (o89*2+ •08) "4 = Co•84 (1.21b4) +1•08)"4=t2167fuca)= (o$9x3+1.08)4 = (089 (1:2167) +1 es) "4 = 1-2f5107= Cofs ry t1-08)"4= (05s c1iz123)+18); 1-2122The rool by ed point levaħauCritenm4 212と=) 1= $(2)1/4x =1.21 22 E(!,2]

Name: Numerical Analysis & it’s applications Q4 only part (ii) of the questi
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Description: Numerical Analysis & it’s applications Q4 only part (ii) of the question needs answering. Part (i) is answered and the answer is included here. Thanks. 4. (Fired-Point Iteration Method;Consider the problem of finding the root of the polynomialf (x) =

Since f(x)=x4-0.89x-1.08 and g(x)=x-f(x)f'(x)=x-x4-0.89x-1.084x3-0.89. So, for fixed point we will…

Math

Advanced Math

(ii) Use the Fixed-Point Iteration method to find an approximation pN of the fixed-point p of g(x) in [1, 2], the root of the polynomial f(x) in [1, 2], satisfying RE(pN = PN-1) < 10-6 by taking po = 1 as the initial approximation. All calculations are to be carried out in the FPA7. Present the results of your calculations in a standard output table for the method of the form RE(pn ~ Pn-1) n Pn-1 Pn

(ii) Use the Fixed-Point Iteration method to find an approximation pN of the fixed-point p of g(x) in [1, 2], the root of the polynomial f(x) in [1, 2], satisfying RE(pN = PN-1) < 10-6 by taking po = 1 as the initial approximation. All calculations are to be carried out in the FPA7. Present the results of your calculations in a standard output table for the method of the form RE(pn ~ Pn-1) n Pn-1 Pn

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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