On the solution of ill‐posed problems by projection methods with a posteriori choice of the discretization level 1

By U. Hämarik, E. Avi, A. Ganina. 2002

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Abstract We consider linear ill‐posed problems Au = ƒ with minimum‐norm solution u*. Instead of ƒ noisy data ƒδ are given satisfying ‖ƒδ — ƒ‖ ≤ δ with known noise level 5. The projection methods for finding approximation un to u* are discussed in assumptions guaranteeing in case ƒδ = ƒ the monotone convergence u n → u* (n → 8). In noisy case δ > 0 we propose for two projection methods a posteriori rules for choice n = n(δ) as largest n = 1,2…, for which inequality ‖un – u*‖ ≤ ‖un_ 1 – u*‖ can be proved. Numerical results are given.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a35675954082db7d16331b69be4f502e5fe44668