[PDF] Top 20 An optimal order yielding discrepancy principle for simplified regularization of ill posed problems in Hilbert scales

... a Hilbert space, then the sim- plified regularization introduced by Lavrentiev is better suited than Tikhonov regularization in terms of speed of convergence and condition number in the case of ... See full document

... Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed oper- ator ... See full document

... the optimal error bound of the problem ...Fourier regularization method with an a prior parameter choice rule has been ...the ill posed problem is usually sensitive to the ... See full document

... I have the deepest gratitude to my advisor, Professor Alexandra Smirnova. I still vividly remember our first seminar about a magnetometric problem in her research group. I was very impressed by the passion for her work ... See full document

... Third, consider a single motion cell (Figure 2). In principle, this cell would be able to sat- isfy the local constraint perfectly. In practice (see Figure 3), the finite output impedance of the p-type Gilbert ... See full document

... a simplified Tikhonov regularization has been presented in ...Tikhonov regularization method to solve the problem ...the regularization parameter can be chosen by a discrepancy ... See full document

... It is a hard work to cluster time series subsequences that are not strictly synchronized and many solutions have been proposed. One straightforward solution is to adjust the phase while the algorithm runs so that the ... See full document

... Since equilibrium problem (.) provides a unified model of several problems such as variational inequalities, fixed point problems and inclusion problems. In [], Takahashi and Takahashi further ... See full document

... in order to solve the ...the regularization parameter choice without the property for j, for the case of demicontinuous or weakly continuous accretive operators A i satisfying ... See full document

... In this work, we give another way for approaching the ill-posedness of an inverse source problem. We deliver a Tikhonov regularization method to consider the above Gaussian random model. The right-hand side ... See full document

... Solving (ill-posed) conditional probability problem instead of pattern recognition prob- lem might appear to contradict this Imperative. However, while estimating conditional probability, one uses prior ... See full document

... inverse problems satis- fying our assumptions on the underlying infinite-dimensional ...mildly ill-posed and a class of severely ill-posed linear inverse prob- lems both in a ... See full document

... y = G(u) + η, η ∼ N (0, Γ), (5.2.1) our quantity of interest is the slowness function. This problem can be attributed as essentially a gradient recovery problem, which has been looked at in a general sense [113, 149, ... See full document

... We now replicate the reconstructions from the previous section but after adding 2% Gaussian noise to the data. The results obtained are shown in Figure 6.10. Once the noise is added, it seems like DCTMC is the preferred ... See full document

... Since the entries of A = A(β) are of order O(β), see (11), we conclude that the error- amplification ratio for the linearized model is of exponential order O(e β ). Is this also the case for the highly ... See full document

... improperly posed problems for partial differential equations, Symposium on Non-Well-Posed Problems and Logarithmic Convexity (Heriot-Watt ... See full document

... Lavrentiev regularization of ill-posed ...the ill-posed equation F (x) = f when the available data is f δ with kf − f δ k ≤ δ and the operator F : D(F ) ⊆ X → X is a nonlinear monotone ... See full document

... such problems can thus become ...such problems and that the error amplification ratio can become very large in the steep but Lipschitz continuous firing rate ... See full document

... In the previous section we present the regularization scheme for Fred- holm integral equation of the first kind. But we can use it for the discrete form of other equations that the matrix of linear system is ... See full document

... proof is accomplished. In particular, the theorem is valid if N is a singleton. Next we will study an operator regularization method for (3.1) with a perturbed right- hand side, perturbed constraint set, and ... See full document