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[en] When functionally graded material layers are inserted between two impedance mismatching media, passbands with extremely large bandwidths can appear in these layered systems. An accurate and effective iterative method is developed to deal with these layered systems with extremely large layer number.
[en] The linear optimization algorithm ART3+O introduced by Chen et al (2010 Med. Phys. 37 4938–45) can efficiently solve large scale inverse planning problems encountered in radiation therapy by iterative projection. Its major weakness is that it cannot guarantee -optimality of the final solution due to an arbitrary stopping criterion. We propose an improvement to ART3+O where the stopping criterion is based on Farkas’ lemma. The same theory can be used to detect inconsistency in other projection methods as well. The proposed algorithm guarantees to find an -optimal solution in finite time. The algorithm is demonstrated on numerical examples in radiation therapy. (paper)
[en] Nekrasov matrices and nonsingular H-matrices are closely related. In this paper, Nekrasov tensors and S-Nekrasov tensors are proved to be nonsingular -tensors. And tensors are generalized Nekrasov tensors if and only if they are nonsingular -tensors. Furthermore, an iterative criterion for identifying nonsingular -tensors is provided.
[en] The characteristic interval plays a vital role on the existence of iterative roots of PM functions with height less than or equal to one. In this paper, we define the characteristic interval for continuous functions and prove theorems on extension and nonexistence of iterative roots for a class of continuous non-PM functions on a closed and bounded interval I. Also, we prove that a class of continuous non-PM functions, which do not possess any iterative roots, is dense in C(I, I).
[en] In this paper we investigate normalization of rational functions, reducing in the sense of conjugation to monomials or more general power functions. We give conditions for the normalization by computing minimal irreducible decomposition of algebraic varieties. We use those conditions to compute the general n-th order iterates and iterative roots for those rational functions.
[en] Fixed point iterations are still the most common approach to dealing with a variety of numerical problems such as coupled problems (multi-physics, domain decomposition, ...) or nonlinear problems (electronic structure, heat transfer, nonlinear mechanics,..). Methods to accelerate fixed point iteration convergence or more generally sequence convergence have been extensively studied since the 1960's. For scalar sequences, the most popular and efficient acceleration method remains the Δ2 of Aitken. Various vector acceleration algorithms are available in the literature, which often aim at being multidimensional generalizations of the Δ2 method. In this paper, we propose and analyse a generic residual-based formulation for accelerating vector sequences. The question of the dynamic use of this residual-based transformation during the fixed point iterations for obtaining a new accelerated fixed point method is then raised. We show that two main classes of such iterative algorithms can be derived and that this approach is generic in that various existing acceleration algorithms for vector sequences are thereby recovered. In order to illustrate the interest of such algorithms, we apply them in the field of nonlinear mechanics on a simplified 'point-wise' solver used to perform mechanical behaviour unit testings. The proposed test cases clearly demonstrate that accelerated fixed point iterations based on the elastic operator (quasi-Newton method) are very useful when the mechanical behaviour does not provide the so-called consistent tangent operator. Moreover, such accelerated algorithms also prove to be competitive with respect to the standard Newton-Raphson algorithm when available. (authors)
[en] This report continues a series of works by the authors on earthquake-prone areas recognition by the algorithmic system FCAZ. For the first time, successive earthquake-prone areas recognition for several magnitude thresholds in the same seismic region is conducted. This can be done by iteratively narrowing the set of recognition objects of the FCAZ system. Earthquake-prone areas for a given magnitude threshold are recognized within zones already recognized as dangerous for a smaller threshold magnitude. The reproducibility of the study is ensured by the fact that at all stages the recognition algorithm remains unchanged. Earthquakeprone areas with magnitude thresholds of М ≥ 5.5, М ≥ 5.75, and М ≥ 6.0 in the Baikal–Transbaikal region are studied successively.