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broyden(x0, fun [,params:params] [, maxit:maxiter] [,minit:miniter]\
  [,criteria:vector(nsigx,nsigfun,dgrad)] [printwhen:d1]\
  [,recordwhen:d2]), REAL vector x0, macro fun(x,i [,params]), integers
  ngold > 0, maxiter >= 0, miniter > 0, nsigx, nsigfun, d1 >= 0, d2 >=
  0, dgrad REAL scalar

Keywords: minimize, quasi-newton, variable metric
Macro broyden() minimizes a function iteratively using a variable metric
algorithm due to Broyden.  It has no linear search step.  See Dahlquist
and Bjorck, Numerical methods, Prentice Hall, 1974, p. 443.

broyden() is a "front-end" to macro minimizer() which it calls with
all the arguments to minimizer() plus argument 'method:"broyden"'.

result <- broyden(x0, fun [, params] [,optional keywords]) computes the
minimum of a real function F(x1,x2,...,xk) starting the Broyden
iteration at x = x0 = vector(x01,x02,...,x0k), a REAL vector with no
MISSING elements.

See minimizer() for details on the arguments, keywords and the value.
Keyword 'golden' is ignored by broyden().

See also minimizer() bfs(), dfp(), and neldermead().

Gary Oehlert 2003-01-15