We show that the condition number of any such p × q submatrix of the N × N DFT matrix is at least , up to algebraic prefactors.

Apr 20, 2020 · Such Vandermonde system matrices arise in many applications, such as Fourier continuation, super-resolution, and diffraction imaging.

Each of our three results is a lower bound on the condition number of contiguous Fourier submatrices that, barring algebraic prefactors, is exponential in the ...

Such Vandermonde system matrices arise in Fourier continuation, super-resolution, and diffraction imaging. Our proof uses the Kaiser-Bessel transform pair, and ...

... Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM Review A. Barnett has provided new bounds on the ...

Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM review A. Barnett has provided new bounds on the ...

How exponentially ill-conditioned are contiguous submatrices of the Fourier matrix? A. Barnett. Linear systems involving contiguous submatrices of the ...

Aug 14, 2020 · The system matrix becomes a p×q Fourier submatrix, with α = 1/SRF, and the exponential blow-up of its conditioning is a fundamental obstacle in ...

How exponentially ill-conditioned are contiguous submatrices of the Fourier matrix? A. Barnett. Mathematics. SIAM Review. 2022. TLDR. The proof uses the Kaiser ...

Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM review A. Barnett has provided new bounds on the ...