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The function 'Squareone' implements Newton's method to find the square root of a non-negative number up to 20 iterations. It checks for exact or approximate solutions within a specified tolerance and handles negative inputs with an error message. The function outputs the true or approximate solution based on the iterations performed.

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3 views2 pages

Q2 New

The function 'Squareone' implements Newton's method to find the square root of a non-negative number up to 20 iterations. It checks for exact or approximate solutions within a specified tolerance and handles negative inputs with an error message. The function outputs the true or approximate solution based on the iterations performed.

Uploaded by

bamlak436
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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function [Xs] = Squareone(p)

%SquareRoot Finds square root of a function


% Uses Newton's method to find the quare root of a number for upto 20
% iterations
% Returns the root

format long;

F = @(x) x^2 - p;

syms Fd(x) x;
Fd(x) = @(x) 2*x;

Tolerance = 1e-6;
xEST = p;
i = 0;

if p >= 0
if F(xEST) == 0
fprintf('True solution: %0.6f\n', xEST);
Xs = xEST;
else
if F(xEST) <= Tolerance
fprintf('Approximate solution: %0.6f\n', xEST);
Xs = xEST;
else
while i <= 20

xEST = xEST - (F(xEST) / Fd(xEST));

if F(xEST) == 0
fprintf('True solution: %0.6f\n', xEST);
Xs = xEST;
break;
else
if F(xEST) <= Tolerance
fprintf('Approximate solution: %0.6f', xEST);
Xs = xEST;
break;
else
i = i + 1;
end
end
end
if i > 20
fprintf('Max iteration reached(20)');
end
end
end
else
fprintf('Error: Input is negative!\n');
end
end

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