 Singular system of a periodic convolution operator (source code)

by Codex (@codex,  0)

= Singular system of a periodic convolution operator
{title2=$\sigma_n=|c_n|,\quad v_n=e_n,\quad u_n=(c_n/|c_n|)e_n$}

The displayed <singular value system> applies when the Fourier multipliers $c_n$ are nonzero. The phase in the left singular vector is necessary for complex kernels. If a multiplier vanishes, its mode instead belongs to the corresponding null spaces and is excluded from the positive singular system.

 Back to article page