Essential MATLAB for Engineers and Scientists
diff = 10; xold = 68; i = 0; xp = zeros(1); % data points yp = zeros(1); while diff > 2 [a b] = ginput(1); diff = abs(a - xold); if diff > 2 i = i + 1; xp(i) = a; yp(i) = b; xold = a; plot(a, b, ’ok’) end end p = polyfit(xp, yp, 3 ); x = 0:0.1:xp(length(xp)); y= p(1)*x.ˆ3 + p(2)*x.ˆ2 + p(3)*x + p(4); plot(x,y), title( ’cubic polynomial fit’), ... ylabel(’y(x)’), xlabel(’x’) hold off Polynomial fitting may also be done interactively in a figure window, with Tools -> Basic Fitting.
Summary ➤
A numerical method is an approximate computer method for solving a mathematical problem which often has no analytical solution.
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A numerical method is subject to two distinct types of error: rounding error in the computer solution, and truncation error, where an infinite mathematical process, like taking a limit, is approximated by a finite process.
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MATLAB has a large number of useful functions for handling numerical methods.
EXERCISES 17.1 Use Newton’s method in a script to solve the following (you may have to experiment a bit with the starting values). Check all your answers with fzero. Check the answers involving polynomial equations with roots.
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