diff --git a/.gitignore b/.gitignore index feb0ccc..e76242b 100644 --- a/.gitignore +++ b/.gitignore @@ -1,33 +1,143 @@ -# ---> MATLAB -# Windows default autosave extension -*.asv +*.ijvm +*.mic1 -# OSX / *nix default autosave extension -*.m~ +# ---> TeX +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc -# Compiled MEX binaries (all platforms) -*.mex* +## Intermediate documents: +*.dvi +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf -# Packaged app and toolbox files -*.mlappinstall -*.mltbx +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.brf +*.run.xml -# Generated helpsearch folders -helpsearch*/ +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync -# Simulink code generation folders -slprj/ -sccprj/ +## Auxiliary and intermediate files from other packages: -# Matlab code generation folders -codegen/ -# Simulink autosave extension -*.autosave +# algorithms +*.alg +*.loa -# Simulink cache files -*.slxc +# achemso +acs-*.bib -# Octave session info -octave-workspace +# amsthm +*.thm +# beamer +*.nav +*.snm +*.vrb + +#(e)ledmac/(e)ledpar +*.end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls + +# gnuplottex +*-gnuplottex-* + +# hyperref +*.brf + +# knitr +*-concordance.tex +*.tikz +*-tikzDictionary + +# listings +*.lol + +# makeidx +*.idx +*.ilg +*.ind +*.ist + +# minitoc +*.maf +*.mtc +*.mtc[0-9] +*.mtc[1-9][0-9] + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# mylatexformat +*.fmt + +# nomencl +*.nlo + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# todonotes +*.tdo + +# xindy +*.xdy + +# WinEdt +*.bak +*.sav + +# Mac stupid tmp files +.DS_Store diff --git a/hw1/hw1.aux b/hw1/hw1.aux deleted file mode 100644 index f23e546..0000000 --- a/hw1/hw1.aux +++ /dev/null @@ -1 +0,0 @@ -\relax diff --git a/hw1/hw1.log b/hw1/hw1.log deleted file mode 100644 index 7ac493d..0000000 --- a/hw1/hw1.log +++ /dev/null @@ -1,165 +0,0 @@ -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 -entering extended mode - 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43 PDF objects out of 1000 (max. 8388607) - 30 compressed objects within 1 object stream - 0 named destinations out of 1000 (max. 500000) - 1 words of extra memory for PDF output out of 10000 (max. 10000000) - diff --git a/hw1/hw1.pdf b/hw1/hw1.pdf index 17a4846..104edd4 100644 Binary files a/hw1/hw1.pdf and b/hw1/hw1.pdf differ diff --git a/hw1/hw1.tex b/hw1/hw1.tex index 38c27a9..511b294 100644 --- a/hw1/hw1.tex +++ b/hw1/hw1.tex @@ -41,6 +41,7 @@ $$ f(100_f) = \frac{1}{1.00 * 10^2} - \frac{1}{(1.00 * 10^2) + 1} = $$\approx (1.00 * 10^{-2}) - (0.99 * 10^{-2}) = 1.00 * 10^{-4} = 0.0001 $$ $$ 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 (0.99 * 10^{-4}) = 0.000099$$ + $$ f(1000_f) = \frac{1}{1.00 * 10^3} - \frac{1}{(1.00 * 10^3) + 1} \approx (1.00 * 10^{-3}) - \frac{1}{1.00 * 10^3} =$$ $$= (1.00 * 10^{-3}) - (1.00 * 10^{-3}) = 0 $$ @@ -54,6 +55,11 @@ $$ g(1000_f) = \frac{1}{(1.00 * 10^3) ((1.00 * 10^3) + 1)} \approx \frac{1}{1.00 f(100_f) & 9.\overline{9009} * 10^{-5} & 9.901 * 10^{-7} & 10^{-2} \\ g(100_f) & 9.\overline{9009} * 10^{-5} & 9.9 * 10^{-9} & 10^{-4} \\ f(1000_f) & 9.99 * 10^{-7} & 9.99 * 10^{-7} & 1 \\ - f(1000_f) & 9.99 * 10^{-7} & 10^{-9} & 10^{-3} \\ + g(1000_f) & 9.99 * 10^{-7} & 10^{-9} & 10^{-3} \\ \end{tabular} +\subsection*{Point d)} +$f(x)$ is clearly less accuratee than $g(x)$ when dealing with floating point numbers. This is largely due to the final +subtraction, since that amplifies approximation errors already introduced in the division $\frac{1}{x + 1}$. Also, the multiplication +in $\frac{1}{x (x + 1)}$ does not cause any approximation errors with the numbers tested, since the mantissa is always 1 and +the multiplication of the exponent part is always exact. \end{document}