hw1 done. Added .gitignore
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# ---> MATLAB
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# Windows default autosave extension
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*.asv
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*.ijvm
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*.mic1
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# OSX / *nix default autosave extension
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*.m~
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# ---> TeX
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## Core latex/pdflatex auxiliary files:
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*.aux
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*.lof
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*.log
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*.lot
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*.fls
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*.toc
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# these rules might exclude image files for figures etc.
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# *.ps
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# *.eps
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# *.pdf
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# Packaged app and toolbox files
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*-blx.aux
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*-blx.bib
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*.brf
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*.run.xml
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## Build tool auxiliary files:
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*.fdb_latexmk
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*.synctex
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*.synctex.gz
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*.synctex.gz(busy)
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*.pdfsync
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# Simulink code generation folders
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slprj/
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sccprj/
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## Auxiliary and intermediate files from other packages:
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# Simulink autosave extension
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*.autosave
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# algorithms
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*.alg
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*.loa
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*.slxc
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# achemso
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acs-*.bib
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# Octave session info
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# amsthm
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*.thm
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# beamer
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*.nav
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*.snm
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*.vrb
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#(e)ledmac/(e)ledpar
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*.end
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*.[1-9]
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*.[1-9][0-9]
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*.[1-9]R
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*.[1-9][0-9][0-9]R
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*.eledsec[1-9]
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*.eledsec[1-9][0-9]R
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*.eledsec[1-9][0-9][0-9]
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*.eledsec[1-9][0-9][0-9]R
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# glossaries
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*.acn
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*.acr
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*.glo
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*.gls
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# gnuplottex
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*-gnuplottex-*
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# hyperref
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*.brf
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*.tikz
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*-tikzDictionary
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# listings
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# makeidx
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*.idx
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*.ilg
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*.ind
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*.ist
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# minitoc
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*.maf
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*.mtc
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*.mtc[0-9]
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*.mtc[1-9][0-9]
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# minted
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_minted*
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*.pyg
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# morewrites
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*.mw
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# mylatexformat
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*.fmt
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# nomencl
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*.nlo
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# sagetex
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*.sagetex.sage
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*.sagetex.py
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*.sagetex.scmd
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# sympy
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*.sout
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*.sympy
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sympy-plots-for-*.tex/
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# TikZ & PGF
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*.dpth
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*.md5
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*.auxlock
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# todonotes
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*.tdo
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# xindy
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*.xdy
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# WinEdt
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*.bak
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*.sav
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# Mac stupid tmp files
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.DS_Store
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@ -1 +0,0 @@
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\relax
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165
hw1/hw1.log
165
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@ -1,165 +0,0 @@
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This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2019.1.23) 3 MAR 2020 21:53
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entering extended mode
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restricted \write18 enabled.
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%&-line parsing enabled.
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**hw1.tex
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(./hw1.tex
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LaTeX2e <2018-04-01> patch level 2
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Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
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File: size12.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
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) (./hw1.aux)
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fb>
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Output written on hw1.pdf (2 pages, 79760 bytes).
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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 $$
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$$ 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$$
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$$ 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}) - (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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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} & 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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\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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