Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Polynomial interpolation and hyperinterpolation over general regions
Journal of Approximation Theory
Implementing Clenshaw-Curtis quadrature, I methodology and experience
Communications of the ACM
Cubature formulae and orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Algorithm 824: CUBPACK: a package for automatic cubature; framework description
ACM Transactions on Mathematical Software (TOMS)
An adaptive numerical cubature algorithm for simplices
ACM Transactions on Mathematical Software (TOMS)
Algorithm 886: Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains
ACM Transactions on Mathematical Software (TOMS)
Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
Numerical Algorithms
| Hi-index | 0.00 |
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 lattice leads to a multivariate DCT. We also present a MATLAB/Octave toolbox which uses this 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.