hw1 done. Added .gitignore
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# ---> MATLAB
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@ -41,6 +41,7 @@ $$ f(100_f) = \frac{1}{1.00 * 10^2} - \frac{1}{(1.00 * 10^2) + 1} =
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$$\approx (1.00 * 10^{-2}) - (0.99 * 10^{-2}) = 1.00 * 10^{-4} = 0.0001 $$
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$$\approx (1.00 * 10^{-2}) - (0.99 * 10^{-2}) = 1.00 * 10^{-4} = 0.0001 $$
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$$ g(100_f) = \frac{1}{(1.00 * 10^2) ((1.00 * 10^2) + 1)} = \frac{1}{1.00 * 10^2 * 1.01 * 10^2} \approx
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(0.99 * 10^{-4}) = 0.000099$$
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(0.99 * 10^{-4}) = 0.000099$$
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$$ f(1000_f) = \frac{1}{1.00 * 10^3} - \frac{1}{(1.00 * 10^3) + 1} \approx
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$$ f(1000_f) = \frac{1}{1.00 * 10^3} - \frac{1}{(1.00 * 10^3) + 1} \approx
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(1.00 * 10^{-3}) - \frac{1}{1.00 * 10^3} =$$
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(1.00 * 10^{-3}) - \frac{1}{1.00 * 10^3} =$$
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$$= (1.00 * 10^{-3}) - (1.00 * 10^{-3}) = 0 $$
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$$= (1.00 * 10^{-3}) - (1.00 * 10^{-3}) = 0 $$
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@ -54,6 +55,11 @@ $$ g(1000_f) = \frac{1}{(1.00 * 10^3) ((1.00 * 10^3) + 1)} \approx \frac{1}{1.00
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f(100_f) & 9.\overline{9009} * 10^{-5} & 9.901 * 10^{-7} & 10^{-2} \\
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f(100_f) & 9.\overline{9009} * 10^{-5} & 9.901 * 10^{-7} & 10^{-2} \\
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g(100_f) & 9.\overline{9009} * 10^{-5} & 9.9 * 10^{-9} & 10^{-4} \\
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g(100_f) & 9.\overline{9009} * 10^{-5} & 9.9 * 10^{-9} & 10^{-4} \\
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f(1000_f) & 9.99 * 10^{-7} & 9.99 * 10^{-7} & 1 \\
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f(1000_f) & 9.99 * 10^{-7} & 9.99 * 10^{-7} & 1 \\
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f(1000_f) & 9.99 * 10^{-7} & 10^{-9} & 10^{-3} \\
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g(1000_f) & 9.99 * 10^{-7} & 10^{-9} & 10^{-3} \\
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\end{tabular}
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\end{tabular}
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\subsection*{Point d)}
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$f(x)$ is clearly less accuratee than $g(x)$ when dealing with floating point numbers. This is largely due to the final
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subtraction, since that amplifies approximation errors already introduced in the division $\frac{1}{x + 1}$. Also, the multiplication
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in $\frac{1}{x (x + 1)}$ does not cause any approximation errors with the numbers tested, since the mantissa is always 1 and
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the multiplication of the exponent part is always exact.
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\end{document}
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\end{document}
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Reference in a new issue