Finite-approximate solvability of Lu = h with exact finite-dimensional constraint π(Lu) = πh holds for all ε > 0 if and only if α T_α^{-1}h → 0 as α → 0⁺.
(2011).An Introduction to the Mathematical Theory of Inverse Problems
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Finite-Approximate Solvability of Linear Operator Equations
Finite-approximate solvability of Lu = h with exact finite-dimensional constraint π(Lu) = πh holds for all ε > 0 if and only if α T_α^{-1}h → 0 as α → 0⁺.