Imported Upstream version 1.72.0

[platform/upstream/boost.git] / libs / math / doc / interpolators / whittaker_shannon.qbk

diff --git a/libs/math/doc/interpolators/whittaker_shannon.qbk b/libs/math/doc/interpolators/whittaker_shannon.qbk
index 701651f..6ae586c 100644 (file)
--- a/libs/math/doc/interpolators/whittaker_shannon.qbk
+++ b/libs/math/doc/interpolators/whittaker_shannon.qbk
@@ -34,10 +34,12 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 [heading Whittaker-Shannon Interpolation]
 
 The Whittaker-Shannon interpolator takes equispaced data and interpolates between them via a sum of sinc functions.
-This interpolation is stable and infinitely smooth, but has linear complexity in the data, making it slow relative to compactly-supported b-splines.
-In addition, we cannot pass an infinite amount of data into the class, and must truncate the (perhaps) infinite sinc series to a finite number of terms.
-Since the sinc function has slow 1/x decay, the truncation of the series can incur large error.
-Hence this interpolator works best when operating on samples of compactly supported functions.
+This interpolation is stable and infinitely smooth, but has linear complexity in the data, 
+making it slow relative to compactly-supported b-splines.
+In addition, we cannot pass an infinite amount of data into the class, 
+and must truncate the (perhaps) infinite sinc series to a finite number of terms.
+Since the sinc function has slow /1/x/ decay, the truncation of the series can incur large error.
+Hence this interpolator works best when operating on samples of compactly-supported functions.
 Here is an example of interpolating a smooth "bump function":
 
     auto bump = [](double x) { if (std::abs(x) >= 1) { return 0.0; } return std::exp(-1.0/(1.0-x*x)); };
@@ -52,7 +54,6 @@ Here is an example of interpolating a smooth "bump function":
         v[i] = bump(t);
     }
 
-
     auto ws = whittaker_shannon(std::move(v), t0, h);
 
     double y = ws(0.3);
@@ -64,6 +65,6 @@ The derivative of the interpolant can also be evaluated, but the accuracy is not
 [heading Complexity and Performance]
 
 The call to the constructor requires [bigo](1) operations, simply moving data into the class.
-Each call the the interpolant is [bigo](/n/), where /n/ is the number of points to interpolate.
+Each call to the interpolant is [bigo](/n/), where /n/ is the number of points to interpolate.
 
 [endsect] [/section:whittaker_shannon]