\relax \newlabel{se*se}{{}{2}} \@writefile{toc}{\contentsline {section}{\numberline {1}Relative and absolute error}{2}} \newlabel{RelAbsErr*se}{{1}{2}} \newlabel{error*se}{{1}{2}} \@writefile{toc}{\contentsline {section}{\numberline {2}Computer arithmetic}{3}} \newlabel{CompArith*se}{{2}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Introducing the standard}{3}} \newlabel{IEEE*se}{{2.1}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Representation of numbers, arithmetic operations}{4}} \newlabel{ieee*se}{{2}{4}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Exceptions}{6}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces \it A program that illustrates some of the features of arithmetic using the IEEE floating point standard.}}{8}} \newlabel{SourcesOfError.C*se}{{1}{8}} \newlabel{TrunkTable*se}{{3}{9}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Estimates of $f^{\prime }(x)$ using (3\hbox {}). The error is $e_{tot}$, which is a combination of truncation and roundoff error. Roundoff error is apparent only in the last two estimates.}}{9}} \@writefile{toc}{\contentsline {section}{\numberline {3}Truncation error}{9}} \newlabel{TruncErr*se}{{3}{9}} \newlabel{fp*se}{{3}{9}} \@writefile{toc}{\contentsline {section}{\numberline {4}Iterative Methods}{9}} \newlabel{IterErr*se}{{4}{9}} \newlabel{ItTable*se}{{4}{10}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Iterates of $x_{n+1} = \mathop {\mathgroup \symoperators ln}\nolimits (y) - \mathop {\mathgroup \symoperators ln}\nolimits (x_n)$ illustrating convergence to a limit that satisfies the equation $xe^x = y$. The error is $e_n = x_n - x$. Here, $y=10$.}}{10}} \newlabel{StatTable*se}{{5}{10}} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Statistical errors in a demonstration Monte Carlo computation.}}{10}} \@writefile{toc}{\contentsline {section}{\numberline {5}Statistical error in Monte Carlo}{10}} \newlabel{StatErr*se}{{5}{10}} \@writefile{toc}{\contentsline {section}{\numberline {6}Error amplification and unstable algorithms}{11}} \newlabel{Stab*se}{{6}{11}} \newlabel{error_amp*se}{{4}{11}} \@writefile{toc}{\contentsline {section}{\numberline {7}Condition number and ill conditioned problems}{12}} \newlabel{Cond*se}{{7}{12}} \newlabel{oneDk1*se}{{5}{13}} \newlabel{kapDef*se}{{6}{13}} \newlabel{oneDk2*se}{{7}{13}} \newlabel{k2*se}{{8}{13}} \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \it A code fragment in which roundoff error can lead to numbers that should be equal in exact arithmetic not being equal in floating point.}}{14}} \newlabel{FloatingPointInequality*se}{{5}{14}} \@writefile{toc}{\contentsline {section}{\numberline {8}Software tips}{14}} \newlabel{Tips*se}{{8}{14}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.1}Floating point numbers are (almost) never equal}{14}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.2}Plotting data curves}{14}} \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \it A code fragment illustrating a pitfall of using a floating point variable to regulate a {\tt while} loop.}}{15}} \newlabel{floatLoopTest*se}{{6}{15}} \@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces \it A code fragment using an integer variable to regulate the loop of Figure 6\hbox {}.}}{15}} \newlabel{intLoopTest*se}{{7}{15}} \@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces \it Plots of the first $n$ Fibonacci numbers, linear scale on the left, log scale on the right}}{16}} \newlabel{PlotScaling*se}{{8}{16}} \@writefile{toc}{\contentsline {section}{\numberline {9}Further reading}{16}} \@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces \it A code fragment using an integer variable to regulate the loop of Figure 6\hbox {}.}}{17}} \newlabel{PlotScalingScript*se}{{9}{17}} \@writefile{toc}{\contentsline {section}{\numberline {10}Exercises}{18}} \newlabel{TF*se}{{1}{18}} \newlabel{Fib*se}{{4}{19}} \newlabel{fibEqn*se}{{9}{19}} \newlabel{Binom*se}{{5}{19}} \newlabel{E(k)*se}{{10}{19}} \newlabel{day}{{6}{20}} \@setckpt{SourcesOfError}{ \setcounter{page}{21} \setcounter{equation}{10} \setcounter{enumi}{6} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{2} \setcounter{mpfootnote}{0} \setcounter{part}{0} \setcounter{section}{10} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{9} \setcounter{table}{0} }