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[lmi-commits] [lmi] master 1f6b5b2b 1/2: Improve documentation
From: |
Greg Chicares |
Subject: |
[lmi-commits] [lmi] master 1f6b5b2b 1/2: Improve documentation |
Date: |
Mon, 18 Apr 2022 17:32:12 -0400 (EDT) |
branch: master
commit 1f6b5b2b7650c1548a9b98959b6e5eb094917fa2
Author: Gregory W. Chicares <gchicares@sbcglobal.net>
Commit: Gregory W. Chicares <gchicares@sbcglobal.net>
Improve documentation
---
zero.hpp | 13 ++++++-------
1 file changed, 6 insertions(+), 7 deletions(-)
diff --git a/zero.hpp b/zero.hpp
index e499a837..5b773f0a 100644
--- a/zero.hpp
+++ b/zero.hpp
@@ -246,13 +246,12 @@ inline double binary64_midpoint(double d0, double d1)
/// function's values only (and not its derivative or functional form)
/// are available." --Press et al., _Numerical Recipes_ (3rd ed. 2007)
///
-/// Numerous papers claim to improve on Brent's method. The best is
-/// ACM Algorithm 748 (Transactions on Mathematical Software):
-///
https://na.math.kit.edu/alefeld/download/1995_Algorithm_748_Enclosing_Zeros_of_Continuous_Functions.pdf
-/// whose Table II compares Brent's algorithm to TOMS748 for fifteen
-/// test problems, claiming an advantage of 4-6%. Chandrupatla
-/// proposed a more stringent criterion for accepting IQI iterates,
-/// and a simplified root-finding method that uses it. However, actual
+/// Numerous papers claim to improve on Brent's method. TOMS 748
+/// purports to require about five percent fewer function evaluations,
+/// but that claim is debunked here:
+/// https://www.nongnu.org/lmi/toms_748.html
+/// Chandrupatla proposed a more stringent criterion for accepting IQI
+/// iterates, and a simplified algorithm that uses it. However, actual
/// measurements (tabulated in Note 4) show that, for the 388 solves
/// in lmi's regression test, Brent's method is best for lmi.
///