Correct TOMS 748 root bracketing docs#1418
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Fixes #1166.
Summary
This is a documentation-only update for the TOMS 748 root-finding docs.
The parameter description now says that the initial bounds must bracket at
least one root, rather than a single root. The
f(a) * f(b) < 0preconditionremains documented immediately below that text.
Rationale
(Alefeld, Potra, and Shi, ACM TOMS 21(3), 1995, DOI:
10.1145/210089.210111).toms748_solverejects same-sign endpoint values, anddetail::bracketupdates the interval by comparing endpoint signs.
f, the endpoint sign change guarantees at least onesign-changing root in the interval. If all roots in the interval are simple
crossings, this implies an odd number of roots, but additional
even-multiplicity roots may also lie in the same bounds, so uniqueness is not
required.
Changes
doc/roots/roots_without_derivatives.qbkdoc/htmlValidation
include/boost/math/tools/toms748_solve.hppand one even-multiplicity root, is accepted
rejected
template is present in the repo or organization-level
.githubrepobuild instructions
b2and initialized the required Boost documentation toolsubmodules/dependencies
../../../b2 -q --user-config=<repo>/user-config.jamfromlibs/math/docgit diff --check