make mathlab code (Secant Method) The Secant method is a classic method for approximating the rootsof a given function (which does not require access to the derivative of the function). Itproduces a sequence of iteratesT1, F2, 13, . . .by the recurrence relationIn - In-1In+1 = Xn - f(x„)-f(In) – f(Tn-1)for n = 2,... where a, and r2 are a pair of unequal initial guesses. There are manyways to decide when to stop the iteration, and in this question, you should stop when|In – In-1| <= TOLwhere TOL is a user supplied tolerance.Notice this stopping criterion is different from the previous problem.secant Function:Input variables:• an anonymous function representing f• a scalar representing the initial guess r1• a scalar representing the initial guess x2• a scalar representing TOLOutput variables:a vector of all iterates produced until the stopping criterion was reached(this vector should include x1 and r2 as its first entries)A possible sample case is:> x = secant (@(x) sin(x), 2, 3, le-8)X =2.00003.00003.18373.14153.14163.14163.1416

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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make mathlab code

(Secant Method) The Secant method is a classic method for approximating the roots
of a given function (which does not require access to the derivative of the function). It
produces a sequence of iterates
T1, F2, 13, . . .
by the recurrence relation
In - In-1
In+1 = Xn - f(x„)-
f(In) – f(Tn-1)
for n = 2,... where a, and r2 are a pair of unequal initial guesses. There are many
ways to decide when to stop the iteration, and in this question, you should stop when
|In – In-1| <= TOL
where TOL is a user supplied tolerance.
Notice this stopping criterion is different from the previous problem.
secant Function:
Input variables:
• an anonymous function representing f
• a scalar representing the initial guess r1
• a scalar representing the initial guess x2
• a scalar representing TOL
Output variables:
a vector of all iterates produced until the stopping criterion was reached
(this vector should include x1 and r2 as its first entries)
A possible sample case is:
> x = secant (@(x) sin(x), 2, 3, le-8)
X =
2.0000
3.0000
3.1837
3.1415
3.1416
3.1416
3.1416

Expert Solution

Step 1

Answer:-

%%Matlab code for finding root using secant clear all close all function for which root have to find a=2; b=3; tol=10^-8; [x]

%%Matlab code for finding root using secant
clear all
close all

%function for which root have to find
a=2;b=3; tol=10^-8;
[x]=secant(@(x) sin(x),a,b,tol)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Matlab function for Secant Method
function [root]=secant(f,x0,x1,tol)
    %f(x1) should be positive
    %f(x0) should be negative
    k=10; count=0;
    root(1)=x0; root(2)=x1;
    while k>tol
        count=count+1;
        xx=double(x1-(f(x1)*((x1-x0)/(f(x1)-f(x0)))));
        x0=x1;
        x1=xx;
        k=abs(x0-x1);
        root(count+2)=xx;
        if count>=1000
                break
        end
    end
end

%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%