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# Chapter 13. Quadrature and Differentiation

Table of Contents

Trapezoidal Quadrature
Gauss-Legendre quadrature
Gauss-Kronrod Quadrature
Double-exponential quadrature
  Overview
  tanh_sinh
  Handling functions with large features near an endpoint with tanh-sinh quadrature
  sinh_sinh
  exp_sinh
  Setting the Termination Condition for Integration
  Setting the Maximum Interval Halvings and Memory Requirements
  Thread Safety
  Caveats
  References
Fourier Integrals
Naive Monte Carlo Integration
Wavelet Transforms
Numerical Differentiation
Automatic Differentiation
Lanczos Smoothing Derivatives

| Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)