On the Stability of Transform-Based Circular Deconvolution
Elliot Linzer · SIAM Journal on Numerical Analysis · 1992
The solution of a set of linear equations involving a circulant matrix is easily accomplished with an algorithm based on fast Fourier transforms. The numerical stability of this algorithm is studied. It is shown that the algorithm is weakly stable; i.e., if the circulant matrix is well conditioned, then the computed solution is close to the exact solution. On the other hand, it is shown that the algorithm is not strongly stable—the computed solution is not necessarily the solution of a nearby circular deconvolution problem.