Spectral method: Difference between revisions

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==== Algorithm ====
 
# Compute the Fourier transform (''b<sub>j,k''</sub>'') of ''g''.
# Compute the Fourier transform (''a<sub>j,k</sub>'') of ''f'' via the formula (*).
# Compute ''f'' by taking an inverse Fourier transform of (''a<sub>j,k''</sub>'').
 
Since we're only interested in a finite window of frequencies (of size ''n'', say) this can be done using a [[fast Fourier transform]] algorithm. Therefore, globally the algorithm runs in {{nowrap|time ''O''(''n'' log ''n'').}}