On the solution of ill‐posed problems by projection methods with a posteriori choice of the discretization level 1
On the solution of ill‐posed problems by projection methods with a posteriori choice of the discretization level 1
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后验选择离散化级别 1 的投影方法求解不适定问题
DOI：
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发表时间：
2002
期刊：
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通讯作者：
A. Ganina
中科院分区：
文献类型：
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作者：
U. Hämarik;E. Avi;A. Ganina
摘要我们考虑线性不适定问题Au = n，具有最小范数解u*.给出满足已知噪声水平为5的δ -≤ δ的带噪声数据δ，而不是带噪声数据。本文讨论了求u ~ n到u ~* 的逼近的投影方法，并给出了在n δ = n时u ~ n → u ~*（n → 8）单调收敛的条件.在噪声δ > 0的情况下，我们提出了两种投影方法选择n = n（δ）作为最大值n = 1，2.的后验规则，并证明了不等式un - u* ≤ un_ 1 - u*。给出了数值结果。
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.