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  than \eqn{\epsilon}{eps *}\eqn{ |x_0| + (tol/3)}, where
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  than \eqn{\epsilon}{eps *}\eqn{ |x_0| + (tol/3)}, where
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  \eqn{\epsilon}{eps} is approximately \code{sqrt(\link{.Machine}$double.eps)}
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  \eqn{\epsilon}{eps} is approximately \code{sqrt(\link{.Machine}$double.eps)}
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  and \eqn{x_0} is the final abscissa \code{optimize()$minimum}.\cr
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  and \eqn{x_0} is the final abscissa \code{optimize()$minimum}.\cr
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  If \code{f} is a unimodal function and the computed values of \code{f}
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  If \code{f} is a unimodal function and the computed values of \code{f}
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  are always unimodal when separated by at least \eqn{\epsilon}{eps *}
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  are always unimodal when separated by at least \eqn{\epsilon}{eps *}
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  \eqn{ |x| + (tol/3)}, then \eqn{x_0} approximates the abcissa of the
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  \eqn{ |x| + (tol/3)}, then \eqn{x_0} approximates the abscissa of the
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  global minimum of \code{f} on the interval \code{lower,upper} with an
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  global minimum of \code{f} on the interval \code{lower,upper} with an
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  error less than \eqn{\epsilon}{eps *}\eqn{ |x_0|+ tol}.\cr
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  error less than \eqn{\epsilon}{eps *}\eqn{ |x_0|+ tol}.\cr
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  If \code{f} is not unimodal, then \code{optimize()} may approximate a
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  If \code{f} is not unimodal, then \code{optimize()} may approximate a
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  local, but perhaps non-global, minimum to the same accuracy.
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  local, but perhaps non-global, minimum to the same accuracy.
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