Integral Approximation Algorithm

A Integral Approximation Algorithm is an numerical approximation algorithm that can be implemented by an integral approximation system (to solve an numerical integration task).

• Example(s):
  • a Steepest-Descent Numerical Integration Algorithm.
  • an Ordinary Differential Equation Algorithm.
  • a Laplacian Algorithm.
  • a Bayesian Quadrature Algorithm.
• See: Deterministic Approximate Bayesian Inference Algorithm.

---

---

References

2016

• http://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html
  • QUOTE: The scipy.integrate sub-package provides several integration techniques including an ordinary differential equation integrator.

>>> help(integrate)
Methods for Integrating Functions given function object.
  quad          -- General purpose integration.
  dblquad       -- General purpose double integration.
  tplquad       -- General purpose triple integration.
  fixed_quad    -- Integrate func(x) using Gaussian quadrature of order n.
  quadrature    -- Integrate with given tolerance using Gaussian quadrature.
  romberg       -- Integrate func using Romberg integration. 

Methods for Integrating Functions given fixed samples.
  trapz         -- Use trapezoidal rule to compute integral from samples.
  cumtrapz      -- Use trapezoidal rule to cumulatively compute integral.
  simps         -- Use Simpson's rule to compute integral from samples.
  romb          -- Use Romberg Integration to compute integral from
                   (2**k + 1) evenly-spaced samples.