Question

Please follow the instructions without using other solutions. Thank you in advance

Let the mathematical function flu) be defined as: f(x)-exp-0.5x)cos(5x) - 0.5 .x>0 Write a Matlab function called Newton1 that would find the zero based on a passing initial guess as an input argument x0. The function returns the estimated zero location x, the function value at the zero location (f) and the number of iteration k. The iteration function converges if f(%) < 5"eps and it should diverge if the iteration number k>10000. When it diverges, it should state so using disp() command. The function should starts as: function [x,fs,k]-Newton1(x0) % enter your code here end Submit the function as a .m file. Test the algorithm to find the zero as follows: >> [x,f,k-Newton!(0) → x = 1.1641, f=-1.6653e-16, k = 7 >>[x,f,k]-Newton1(0.1)x 0.1972, f-1.1102e-16, k-5 >>[xf,k]-Newton 1(1.5)x 1.3111 >> [x,f,k-Newton 1 (2) → warning iteration diverged, x = 2.8808, f=-0.5624, k = 10001 f--1.1102e-16, k- 6

Answer 1

function [x f k]=Newton1(x0)

k=0;
% find intial values
xk=x0-(exp(-0.5*x0)*cos(5*x0)-0.5)/(-5*exp(-0.5*x0)*sin(5*x0)-0.5*exp(-0.5*x0)*cos(5*x0))

while abs(xk-x0)>5*eps % while loop toitertations
  

x0=xk;
  
xk=x0-(exp(-0.5*x0)*cos(5*x0)-0.5)/(-5*exp(-0.5*x0)*sin(5*x0)-0.5*exp(-0.5*x0)*cos(5*x0))

  
  
if k>10000
disp('Warning,Iteration diverged')
return
end
k=k+1
  
end
x0=xk
f=(exp(-0.5*x0)*cos(5*x0)-0.5)
x=xk

end

  

MATLAB R2015a HOME EDITOR Find Files Run Section compare ▼ 'Vİ Print Go To ▼ Comment 96骝 New Open Save Breakpoints Run Run and Advance Advance Run and Find Current Folderⓡ 反Editor-C:\UsersAadhyaDesktopNewton1.m Newton1.m+ 困Li-Projec ^ 困 ANSYS , function [x f k]=Newton1(X0) ANSYS Ansys 1… DAES 田 困 : EGT 田 : goa 田 : harry p 困」IC 困_IMAT 田 : john w kashy... 」KT 困 困 KT Sern.. Details 1.1641 Name O Type here to search 3:44 PM 4/1/2019 兵

MATLAB R2015a HOME PLOTS EDITOR Find Files Run Section compare ▼ 'Vİ Print Go To ▼ Comment a New Open Save Breakpoints Run Run and Advance Advance Run and Find Indent Time Current Folder Editor-CA aDesktop Newton1.nm Proj9 hile abs (xk-x0)>5*eps while loop toitertation 困 ANSYS , 10 ANSYS 田 | Ansys 1 11 DAES 13 困 : EGT 田 : goa Command Windovw harry 困」IC 困_IMAT 田 : john w 2.3746 kashy... 」KT 困 困 KT Sern.. 10001 Details Name 2.6841 Warning,Iteration diverged Error in Newton1 (line 3) Output argument "x" (and maybe othera) not assigned during call to "Newtoni Newton1 Ln 32 Col5 O Type here to search 3:45 PM 4/1/2019 41)