@Article{Poppe:2013:CMO,
  author =       "Koen Poppe and Ronald Cools",
  title =        "{CHEBINT}: a {MATLAB/Octave} toolbox for fast 
                  multivariate integration and interpolation based on 
                  {Chebyshev} approximations over hypercubes",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "40",
  number =       "1",
  year =         "2013",
  month =        oct,
  pages =        "2:1--2:13",
  url =          "http://doi.acm.org/10.1145/2513109.2513111",
  accepted =     "13 March 2013",
  abstract =     "
                  We present the fast approximation of multivariate
                  functions based on Chebyshev series for two types
                  of Chebyshev lattices and show how a fast Fourier
                  transform (FFT) based discrete cosine transform
                  (DCT) can be used to reduce the complexity of this
                  operation. Approximating multivariate functions
                  using rank-$1$ Chebyshev lattices can be seen as
                  a one-dimensional DCT while a full-rank Chebyshev
                  lattices leads to a multivariate DCT.

	          We also present a MATLAB/Octave toolbox which uses
	          the above fast algorithms to approximate functions
	          on a axis aligned hyper-rectangle. Given a certain
	          accuracy of this approximation, interpolation
	          of the original function can be achieved by
	          evaluating the approximation while the definite
	          integral over the domain can be estimated based
	          on this Chebyshev approximation. We conclude with
	          an example for both operations and actual timings
	          of the two methods presented.",
}