Truncated singular value decomposition

For a singular value decomposition $A{v}_j={\sigma }_j{u}_j$, truncated SVD with cutoff $\tau >0$ estimates the inverse action by $x_{\tau }={\sum }_{{\sigma }_j\ge \tau }{\sigma }_j^{-1}⟨b,u_j⟩v_j$. Discarding small singular values limits amplification of data errors; this is a spectral regularization method.

Truncated singular value decomposition retains only singular components above a threshold, or equivalently only a finite leading set of singular vectors.