vectorized uni-root?

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.varadhan at jhu.edu>
To: "'ivo.welch at gmail.com'" <ivo.welch at gmail.com>
Cc: "r-help at r-project.org" <r-help at r-project.org>
Subject: Re: [R] vectorized uni-root?
Message-ID:
	<2F9EA67EF9AE1C48A147CB41BE2E15C32E8D67 at 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