Question

Write a line search Secant methods for solving f(x)=0 and implement the algorithms for solving the x^2-1=0 in Matlab Programming.

Answer 1

%%Matlab code for secant method for finding root clear all close all %function for which root have to find f-e (x) x.*2-1; tinitial guess x0 0 x1-2; root, count] secant_method (f,x0, xl); displaying the function fprintf 'For the function f(x) disp(f) fprint f ( The root of the function using Secant method is %f.\n", root) Matlab function for Secant Method function [root,count]-secant_method (fun, x0,x1) %f(x1) should be positive %f(x0) should be negative k-10; count-0; while k>10A-6 count=count+ 1 ; x0-x1; k-abs (fun(xx) end root-xx; end For the function f(x)- (x)x. 2-1 The root of the function using Secant method is 1.000000. Published with MATLAB® R2018a

%%Matlab code for Secant method for finding root
clear all
close all
%function for which root have to find
f=@(x) x.^2-1;
%initial guess
x0=0;x1=2;
[root,count]=secant_method(f,x0,x1);
%displaying the function
fprintf('For the function f(x)=\n')
disp(f)
fprintf('The root of the function using Secant method is %f.\n',root)

%Matlab function for Secant Method
function [root,count]=secant_method(fun,x0,x1)
%f(x1) should be positive
%f(x0) should be negative
k=10; count=0;
while k>10^-6
    count=count+1;
    xx=double(x1-(fun(x1)*abs((x1-x0)/(fun(x1)-fun(x0)))));
    x0=x1;
    x1=xx;
    k=abs(fun(xx));
end
root=xx;
end

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