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author | zimmerma <zimmerma@211d60ee-9f03-0410-a15a-8952a2c7a4e4> | 2012-10-05 15:44:56 +0000 |
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committer | zimmerma <zimmerma@211d60ee-9f03-0410-a15a-8952a2c7a4e4> | 2012-10-05 15:44:56 +0000 |
commit | 758d5be99c21d2cf31528d24bcdb373868c307f0 (patch) | |
tree | ab5bc5a51db50a023c2a4825457c5b1cf9c621c8 /doc | |
parent | e0b0bf3099ab41af19ef0dac3cbae9f67d733793 (diff) | |
download | mpc-758d5be99c21d2cf31528d24bcdb373868c307f0.tar.gz |
[algorithms.tex] improve the range for the error bound of mpc_sqrt
git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1283 211d60ee-9f03-0410-a15a-8952a2c7a4e4
Diffstat (limited to 'doc')
-rw-r--r-- | doc/algorithms.tex | 4 |
1 files changed, 4 insertions, 0 deletions
diff --git a/doc/algorithms.tex b/doc/algorithms.tex index 810d06d..3ab0849 100644 --- a/doc/algorithms.tex +++ b/doc/algorithms.tex @@ -1033,6 +1033,10 @@ there is $0 < \xi < \epsilon_1$ with \end {equation} For instance $\epsilon \leq \epsilon_1$ for $\epsilon_1 \leq \frac {3}{4}$. +We even have $\epsilon \leq \epsilon_1$ for $\epsilon_1 \leq 1$, +since $1 - \sqrt{1-x}$ is bounded by $x$ +for $0 < x \leq 1$, which comes from $1 - x \leq \sqrt{1-x}$. + \subsubsection {Logarithm} |