Spectral regularization method

A spectral regularization method applies a bounded scalar filter to the spectrum of

A^{*} A

. In a singular system of a compact operator, it has the form

R_{α} f = \sum_{j} g_{α} (σ_{j}^{2}) σ_{j} ⟨ f, u_{j} ⟩ v_{j},

where the filters approximate

1/ λ

while controlling amplification near

λ = 0

.

Table of contents
- Truncated singular value decomposition Spectral regularization method

Truncated singular value decomposition

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

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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 326 / 1 / 1 / 3 / a / Solution

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