Reconstruction of a discontinuous function from a few Fourier coefficients using Bayesian estimation
Journal of Scientific Computing
On the Gibbs Phenomenon and Its Resolution
SIAM Review
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
Journal of Computational Physics
Towards the resolution of the Gibbs phenomena
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Inverse Polynomial Reconstruction of Two Dimensional Fourier Images
Journal of Scientific Computing
| Hi-index | 31.45 |
We generalize the Inverse Polynomial Reconstruction Method (IPRM) for mitigation of the Gibbs phenomenon by reconstructing a function from its m lowest Fourier coefficients as an algebraic polynomial of degree at most n-1(m=n). We compute approximate Legendre coefficients of the function by solving a linear least squares problem. We show that if m=n^2, the condition number of the problem does not exceed 2.39. Consequently, if m=n^2, the convergence rate of the modified IPRM for an analytic function is root exponential on the whole interval of definition. Numerical stability and accuracy of the proposed algorithm are validated experimentally.