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Inverse problem

Normal equation for a linear inverse problem

{c}

For a compact operator with singular system $(\sigma_j,u_j,v_j)$, the datum $f$ lies in the domain of $A^\dagger$ exactly when its component in $\overline{\operatorname{ran}A}$ satisfies
$$
\sum_j\frac{|\langle f,u_j\rangle|^2}{\sigma_j^2}<\infty.
$$

Picard criterion

Admissible data for a periodic convolution inverse

Moore–Penrose inverse of an operator

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 70 / 4 / c / i / Solution

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Strong convergence of relaxed Landweber iteration

Picard criterion

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Picard criterion

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