Solution for Ex 1. On the script Esercizio1 write: 1

(1)

Solution for Ex 1. On the script Esercizio1 write:

1

^{clear all}

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^{close all}

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% the first function

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f=@ (x) (1+x.^2) ;

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^{a=0; b=1;}

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sol=quad(f,0,1); %true solution

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^{m = 5;}

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[x,w]= SimpsonComposto(m,a,b) ;

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S_CS=sum(w.*f(x));

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disp('Error for Simpson')

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^abs(S_CS

−

sol)

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x2 = linspace(0,1,11);

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^{m = 10;}

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I=TrapezioComposto(f,a,b,x2,m);

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disp('Error for trapezio')

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^abs(I

−

sol)

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% the second function

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f=@ (x) (1/8+2*x) ;

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^{a=0; b=1;}

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sol=quad(f,0,1); %true solution

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^m=5;

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[x,w]= SimpsonComposto(m,a,b) ;

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S_CS=sum(w.*f(x));

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disp('Error for Simpson')

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^abs(S_CS

−

sol)

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x2 = linspace(0,1,11);

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^{m = 10;}

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I=TrapezioComposto(f,a,b,x2,m);

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disp('Error for trapezio')

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^abs(I

−

sol)

1

(2)

Solution for Ex 2. Write the function 1

^function [L, U] = LUnoPiv(A)

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% LU factorization without pivoting

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n = size(A,1); % size of A

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L = eye(n); % initialize

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^for ^{k = 1:n}

−

1

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^for ^{i = k+1:n}

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% multipliers for gaussian elimination

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L(i,k) = A(i,k)/A(k,k);

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^for ^{j = k:n}

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% construct A

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^{A(i,j) =} ^A(i,j)

−

L(i,k)*A(k,j);

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^end

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^end

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^end

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^{U = A;}

2

 Solution for Ex 1. On the script Esercizio1 write: 1