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In this paper, a regularized sampling algorithm for band-limited signals is presented in the twodimensional case. The convergence of the regularized sampling algorithm is studied and compared with Shannon's sampling theorem and the Tikhonov regularization method by some examples. [ABSTRACT FROM AUTHOR]

In this paper, we aim to calibration pricing models from market prices. We investigate the problem of calibrating the parameters using the trust region method from given price data. We start with the Hull-White model and formulate the problem by obtaining the first kind integral equation, and then consider the parameter recovery problem of the Black-Scholes model. We apply trust region algorithm for numerical retrieval problems. Numerical simulations are given to illustrate the feasibility of our proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to reconstructing initial tsunami waveforms in tsunami source areas based on the inversion of remote measurements of water-level data. This inverse problem is treated as an ill-posed problem of hydrodynamic inversion with tsunami tide gauge records. Tsunami wave propagation is considered within the scope of the linear shallow-water theory. The direct problem is approximated by a finite-difference technique. The ill-posed inverse problem of reconstructing initial tsunami waveforms is regularized by means of a least square inversion using the truncated SVD approach. A so-called r-solution is numerically obtained. The algorithm is verified with real bathymetry data of the Peru subduction zone and synthetic records. It is found that the accuracy of tsunami source reconstruction strongly depends on the signal-to-noise ratio, the azimuthal and temporal coverage of tide gauge stations relative to the target area and the bathymetric features along the wave path. [ABSTRACT FROM AUTHOR]

In this paper, the possibility of using the reverse connection control for iteratively regularized Gauss–Newton-type algorithms is analyzed. It is shown that for the generalized Gauss–Newton iterations the diameter of the set containing the control elements can tend to ∞ as n → ∞. To further improve the stabilizing properties of the Gauss–Newton scheme, a new penalty term is proposed that can depend nonlinearly on the current iteration. As a test numerical example, a nonlinear inverse scattering problem of computing a 2D obstacle shape is considered. [ABSTRACT FROM AUTHOR]

The preconditioned iteratively regularized Gauss–Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (Inverse Problems 23: 1547–1563, 2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes ℳ-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented. [ABSTRACT FROM AUTHOR]