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Superior to the other well-known iterations, such as Landweber iteration, total variational regularization is a well-established method for identifying the piecewise smooth parameter and processing the image. Therefore, we propose a new iteratively total variational regularization based on total variational regularization and homotopy perturbation technique in this paper. Taking advantage of Bregman distance, we construct a nested iteration to inverse parameters. Meanwhile we prove that the error of the new method decreases monotonically, and the new iterative method with the noisy data is regular according to the discrepancy principle. In the last numerical section, compared with Landweber type total variational regularization and Runge–Kutta type regularization, numerical results of this new method indicate that this new regularization is time saving for the same accuracy, and more robust to the noisy data. [ABSTRACT FROM AUTHOR]

In this paper, a method with very high order of convergence is constructed and analyzed. The method is used to compute generalized inverses. The efficiency index has been employed to show its superiority. Numerical experiments re-verify that the proposed iterative expression is more effective than the existing methods of the same type. [ABSTRACT FROM AUTHOR]

Many physics problems can only be studied by coupling various numerical codes, each modeling a subaspect of the physics problem that is addressed. In most cases, the “brute force” technique of running the codes one after the other in a loop until convergence is reached requires excessive CPU time. The present paper illustrates that re-writing the coupling as a root-finding problem, to which a quasi-Newton method–here the (Inverse) Column Updating Method–can be applied, is useful to push down the computation time, at the expense of a very modest amount of supplementary programming. A simplified version of the set of codes commonly used to describe plasma heating by radio frequency waves in a tokamak plasma is adopted for illustrating the potential of the speed-up method. It consists of a wave equation as well as a Fokker–Planck velocity space diffusion and a radial energy diffusion model. It is shown that with this approach a substantial reduction in CPU time needed for convergence can be obtained. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we construct a Runge–Kutta type total variation regularization for the nonlinear ill-posed problems. This method resembles Runge–Kutta type iteration with the Bregman distance as a regularization functional. In the presence of noise with noise level we prove this method to be convergent under appropriate stopping rule. Furthermore, some numerical experiments are presented to verify this method to be more suitable for problems with discontinuous solutions. [Copyright &y& Elsevier]

Abstract: We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata. In this paper, we propose several iterative schemes based on the alternating direction method of multipliers for solving the nonnegative inverse problem. We also extend our schemes to the symmetric case and the cases of prescribed lower bounds and of prescribed entries. Numerical tests (including a practical engineering application in vibrations) show the efficiency of the proposed iterative schemes. [Copyright &y& Elsevier]

Abstract: We investigate the potential of sparsity constraints in the electrical impedance tomography (EIT) inverse problem of inferring the distributed conductivity based on boundary potential measurements. In sparsity reconstruction, inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting -penalty term. The functional is minimized with an iterative soft shrinkage-type algorithm. In this paper, the feasibility of the sparsity reconstruction approach is evaluated by experimental data from water tank measurements. The reconstructions are computed both with sparsity constraints and with a more conventional smoothness regularization approach. The results verify that the adoption of -type constraints can enhance the quality of EIT reconstructions: in most of the test cases the reconstructions with sparsity constraints are both qualitatively and quantitatively more feasible than that with the smoothness constraint. [Copyright &y& Elsevier]