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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
$$
\sum_j\frac{|\langle f,v_j\rangle|^2}{\sigma_j^2}<\infty.
$$

Picard criterion

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 326 / 3 / e / Solution

Picard criterion

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Picard criterion

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