The package rootoned on http://r-forge.r-project.org/R/?group_id=395
has an all-R version of zeroin (the algorithm of uniroot). This should
also be in Rmpfr by Martin M., as it was set up for that use. I suspect
it can be vectorized fairly easily. However, it may be simpler to write,
or else abstract from that code, a vectorized false position or secant
code (same formula, FP must have end points with opposite sign function
values, so is `safer'). This avoids the bisection step and simplifies
things, but may be a bit less efficient sometimes.
JN
Date: Fri, 9 Nov 2012 14:58:55 +0000
From: Ravi Varadhan <ravi.varad...@jhu.edu>
To: "'ivo.we...@gmail.com'" <ivo.we...@gmail.com>
Cc: "r-help@r-project.org" <r-help@r-project.org>
Subject: Re: [R] vectorized uni-root?
Message-ID:
<2f9ea67ef9ae1c48a147cb41be2e15c32e8...@dom-eb-mail1.win.ad.jhu.edu>
Content-Type: text/plain
Hi Ivo,
The only problem is that uniroot() actually uses Brent's algorithm, and
is based on the C code from netlib (there is also Fortran code available
- zeroin.f). Brent's algorithm is more sophisticated than a simple
bisection approach that you have vectorized. It combines bisection and
secant methods along with some quadratic interpolation. The idea behind
this hybrid approach (which by the way is a fundamental theme in all of
numerical analysis) is to get faster convergence while not sacrificing
the global convergence of bisection.
So, the existing uniroot() will not be deprecated unless you can
vectorize Brent's hybrid root-finding approach!
Best,
Ravi
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