Minor cleanup of minimaxApprox and plot documentation.

man/MiniMaxApprox.Rd

@@ -50,14 +50,14 @@ minimaxApprox(fn, lower, upper, degree, relErr = FALSE, xi = NULL,
             \code{maxiter}.
             \item \code{showProgress}: logical; If \code{TRUE} will print error
             values at each iteration.
-             \item \code{convRatio}: numeric; The convergence ratio tolerance.
-             Defaults to \code{1+1e-9}. See \strong{Details}.
-             \item \code{tol}: numeric; The absolute difference tolerance.
-             Defaults to \code{1e-14}. See \strong{Details}.
-             \item \code{tailtol}: numeric; The tolerance of the coefficient of
-             the largest power of \code{x} to be ignored when performing the
-             polynomial approximation a second time. Defaults to \code{1e-10}.
-             See \strong{Details}.
+            \item \code{convRatio}: numeric; The convergence ratio tolerance.
+            Defaults to \code{1+1e-9}. See \strong{Details}.
+            \item \code{tol}: numeric; The absolute difference tolerance.
+            Defaults to \code{1e-14}. See \strong{Details}.
+            \item \code{tailtol}: numeric; The tolerance of the coefficient of
+            the largest power of \code{x} to be ignored when performing the
+            polynomial approximation a second time. Defaults to \code{1e-10}.
+            See \strong{Details}.
         }
     }
 }
@@ -69,42 +69,43 @@ as described by Cody et al. (1968). Convergence is considered achieved when all
 three of the following criteria are met:
     \enumerate{
         \item The observed error magnitudes are within tolerance of the expected
-         error (Distance Test).
-        \item The observed error magnitudes are within tolerance of each other
-        (Magnitude Test).
-        \item The observed error signs oscillate (Oscillating Test).
+         error---the \strong{Distance Test}.
+        \item The observed error magnitudes are within tolerance of each
+        other---the \strong{Magnitude Test}.
+        \item The observed error signs oscillate---the
+        \strong{Oscillation Test}.
     }
 \dQuote{Within tolerance} can be met in one of two ways:
     \enumerate{
         \item The difference between the absolute magnitudes is less than or
         equal to \code{tol}.
-        \item The ratio between the larger and smaller is less than or equal to
-        \code{convRatio}.
+        \item The ratio between the absolute magnitudes of the larger and
+        smaller is less than or equal to \code{convRatio}.
     }
 
-For efficiency, the Distance Test is taken between the absolute value of the
-largest observed error and the absolute value of the expected error. Similarly,
-the Magnitude Test is taken between the absolute value of the largest observed
-error and the absolute value of the smallest observed error. Both the Magnitude
-Test and the Distance Test can be passed by \strong{either} being within
-\code{tol} or \code{convRatio} as described above.
+For efficiency, the \strong{Distance Test} is taken between the absolute value
+of the largest observed error and the absolute value of the expected error.
+Similarly, the \strong{Magnitude Test} is taken between the absolute value of
+the largest observed error and the absolute value of the smallest observed
+error. Both tests can be passed by \strong{either} being within \code{tol} or
+\code{convRatio} as described above.
 }
 \subsection{Polynomial Evaluation}{
 The polynomials are evaluated using the Compensated Horner Scheme of Langlois et
-al. (2006) to enhance both stability and precision at the expense of some speed.
+al. (2006) to enhance both stability and precision.
 }
-\subsection{Polynomial Algorithm Singular Error Response}{
+\subsection{Polynomial Algorithm \dQuote{Singular Error} Response}{
 When too high of a degree is requested for the tolerance of the algorithm, it
 often fails with a singular matrix error. In this case, for the polynomial
 version, the algorithm will try looking for an approximation of degree
 \code{n + 1}. If it finds one, \strong{and} the contribution of that coefficient
-to the approximation is \eqn{\le}\code{tailtol}, it will ignore that coefficient
-and return the resulting degree \code{n} polynomial, as the largest coefficient
-is effectively 0. The contribution is measured by multiplying that coefficient
-by the endpoint with the larger absolute magnitude raised to the \code{n + 1}
-power. This is done to prevent errors in cases where a very small coefficient is
-found on a range with very large absolute values and the resulting contribution
-to the approximation is \strong{not} \emph{de minimis}.
+to the approximation is \eqn{\le} \code{tailtol}, it will ignore that
+coefficient and return the resulting degree \code{n} polynomial, as the largest
+coefficient is effectively 0. The contribution is measured by multiplying that
+coefficient by the endpoint with the larger absolute magnitude raised to the
+\code{n + 1} power. This is done to prevent errors in cases where a very small
+coefficient is found on a range with very large absolute values and the
+resulting contribution to the approximation is \strong{not} \emph{de minimis}.
 }
 }
 \value{

man/plot.minimaxApprox.Rd

@@ -9,7 +9,7 @@
 
 \description{
 Produces a plot of the error of the \code{"minimaxApprox"} object, highlighting
-the basis points and error bounds.
+the basis points and the error bounds.
 }
 
 \usage{\method{plot}{minimaxApprox}(x, y, \dots)}