Solution for Ex 1. Write the following functions.

(1)

Solution for Ex 1. Write the following functions.

1

^function [x,iter] = bisection(f,a,b,tol,maxiter)

2

%BISECTION for finding zeros of functions

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res = tol+1; iter = 0; % Initialize

4

^while res > tol && iter < maxiter

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c = (a+b)/2;

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^if ^{f(c) == 0}

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^{x = c;} ^break;

8

^elseif f(c)*f(a) < 0

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^{b = c;}

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^elseif f(c)*f(b) < 0

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^{a = c;}

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^end

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res = abs(f(c)); iter = iter+1;

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^end

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^{x = c;}

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^if iter >= maxiter

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disp('no convergence iter > maxiter')

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^end

1

^function [x,iter] = newton(f,fp,x0,tol,maxiter)

2

%NEWTON for finding zeros of functions

3

res = tol+1; iter = 0; % Initialize

4

^while res > tol && iter < maxiter

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^{x0 = x0}

−

f(x0)/fp(x0);

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res = abs(f(x0)); iter = iter+1;

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^end

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^{x = x0;}

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^if iter >= maxiter

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disp('no convergence iter > maxiter')

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^end

1

(2)

Solution for Ex 2. On the script named Esercizio2 write the following code.

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^{clear all}

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^{close all}

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^clc

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format long

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f = @(x) exp(x)

−

_4*x.^2;

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x = linspace(

−

2,5);

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^figure

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^{hold on}

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^{grid on}

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plot(x,f(x))

-2 -1 0 1 2 3 4 5

-20 -10 0 10 20 30 40 50

1

fp = @(x) exp(x)

−

_8*x;

2

x1 = bisection(f,

−

1,0,1.e

−

06,50)

3

x2 = newton(f,fp,1,1.e

−

06,50)

4

^{x1 =}

−

0.407776832580566

5

x2 = 0.714805912364580

2

 Solution for Ex 1. Write the following functions.