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• W2802348655 abstract "In the fruitful Autumn, by the side of beautiful West Lake, The Sixth International Conference on Numerical Algebra and Scientific Computing (NASC 2016) was held during October 22–26, 2016, in Zhejiang Hotel, Hangzhou, one of the most attractive cities in China, just as the old Chinese saying goes, “In the heaven there is paradise, on earth Suzhou and Hangzhou.” About 220 participants attended NASC 2016, coming from more than 10 countries including Australia, Canada, China, Czech Republic, France, Germany, Russia, Sweden, UK, and USA. Among them there were eight invited keynote speakers, 30 contributed speakers, and 18 poster presentations. This issue of the journal “Numerical Linear Algebra with Applications” contains carefully selected and peer-reviewed articles by the speakers and by the scientific and organizing committee members of the conference. The conference was organized by the Chinese Academy of Sciences and supported by Zhejiang University. The organizing committee consisted of Zhong-Zhi Bai from the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing; Dan-Fu Han from the Hangzhou Normal University, Hangzhou; Zheng-Da Huang and Qing-Biao Wu both from the Zhejiang University, Hangzhou; and Shi-Jun Yang from the Zhejiang Gongshang University, Hangzhou. The purpose of the conference was to provide a high-level and friendly platform for experts in numerical algebra and scientific computing to report state-of-the-art research results, exchange new ideas, and discuss future developments. The talks demonstrate the present activity in these areas and illustrate the diversity of the ongoing research. The topics discussed include preconditioning and iterative methods for large sparse systems of linear and nonlinear equations such as standard and generalized saddle-point problems, for least-squares problems in matrix and tensor forms, for linear and nonlinear matrix equations such as algebraic Riccati equations, and for linear and nonlinear eigenvalue problems; modulus-based matrix splitting iteration methods for linear and nonlinear complementarity problems; sinc discretizations for linear ordinary differential equations; fast preconditioned and iterative methods for fractional partial differential equations; and sparse and structured matrix computations, as well as parallel computing. Applications to computational fluid dynamics, image restoration, elliptic optimal control, computerized tomography image reconstruction, and liquid crystal modelling were presented. As an important academic event during the conference, the Applied Numerical Algebra (ANA) Prize was awarded to Dr. Zhi-Ru Ren from the School of Statistics and Mathematics, Central University of Finance and Economics, Beijing; and an honorable mentioning was given to Dr. Ju-Li Zhang from the School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai. The ANA Prize is awarded at every NASC conference to, at most, two academic papers written by Chinese scientists of age under 35, working in the field of applied numerical algebra in China and having obtained a Master's or Doctoral degree within the last 5 years. We are happy to have been able to secure manuscripts at the leading edge of research on numerical algebra and scientific computing from eight of the speakers at the conference, and we hope that readers of this issue will enjoy the contributions as much as we have. Here, we remark that these eight papers are ordered according to their online publication dates. Bai1 establishes a class of exact and inexact quasi-HSS iteration methods and discusses their convergence properties for large sparse non-Hermitian positive definite linear systems. Experimental results are given to show that both iteration methods are effective and robust when they are used either as linear solvers or as matrix splitting preconditioners for the Krylov subspace iteration methods. In addition, these two iteration methods are, respectively, much more powerful than the exact and inexact HSS iteration methods, especially when the linear systems have nearly singular Hermitian parts or strongly dominant skew-Hermitian parts, and they can be employed to solve non-Hermitian indefinite linear systems with only mild indefiniteness. Zhang et al.2 propose an efficient approach for solving a linear ill-posed inverse problem with total variation regularization and illustrate its effectiveness by experimental results on image restoration applications. Frommer et al.3 look at bounds for the entries of functions of matrices. For the matrix inverse, and more generally for Cauchy–Stieltjes functions, and for certain normal matrices A including shifted Hermitian and skew-Hermitian matrices, they develop quite sharp bounds for these entries. The bounds show that the size of the entries f (A)i j decreases exponentially with the distance of i and j in the graph of A. For solving a class of elliptic optimal control problems with pointwise box constraints on the control, Song et al.4 propose an infinite-dimensional inexact ADMM as Phase-I algorithm. The two inner subproblems are discretized by two different types of finite element schemes, so that one of the discretized subproblems has a closed-form solution and the other can be solved efficiently by the PMHSS-preconditioned GMRES method. To increase the accuracy, the primal–dual active set method is used as Phase-II algorithm. Theoretical and numerical results are given to show the effectiveness of the proposed method. Wang et al.5 propose a structure-preserving preconditioner and a circulant preconditioner for the Toeplitz-like discretized linear systems arising from the space-fractional coupled nonlinear Schrödinger equations, so that the Krylov subspace iteration methods such as BiCGSTAB can converge very quickly when used to solve the corresponding preconditioned linear systems. In order to improve the performance of the HSS preconditioner for the non-Hermitian positive definite system of linear equations, Yang6 proposes an efficient scaled norm minimization method to compute the parameter additionally introduced in the HSS preconditioner, obtaining a two-parameter HSS preconditioner. As a result, an effective and practical formula for the parameter is derived, which shows good performance in the numerical implementations. For the generalized saddle-point problems, Zhang7 presents an efficient variant of the HSS preconditioner and shows that this new preconditioner is much closer to the generalized saddle point matrix and easier to be implemented than the HSS preconditioner. The solution of linear discrete ill-posed problems requires regularization to avoid severe error propagation. In Tikhonov regularization, a penalty term is used to damp spurious oscillations of the computed solution. Dykes et al.8 discuss the construction of penalty terms that are determined by solving a matrix-nearness problem. These penalty terms allow partial transformation to the standard form of Tikhonov regularization problems that stem from the discretization of integral equations on a cube in several space dimensions. Finally, we would like to take this opportunity to thank the sponsors of the conference: the School of Mathematical Sciences, Zhejiang University; AMSS, Chinese Academy of Sciences; the School of Science, Hangzhou Normal University; and the School of Statistics and Mathematics, Zhejiang Gongshang University. Our special thanks go to Dr. Cun-Qiang Miao and Dr. Kang-Ya Lu, and Dr. Ping-Fei Dai, Dr. Wen-Li Liu, Dr. Yun Liu, Dr. Hui-Di Wang, and Dr. Yu-Xi Wu, as well as Ms. Min Wei (from AMSS), Jia-Qi Chen, Li-Xia Ye, Ya-Ru Zhang, and others for their enthusiasm and help with the organization of the conference." @default.
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• W2802348655 date "2018-04-16" @default.
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• W2802348655 title "Editorial: Novel methods and theories in numerical algebra with interdisciplinary applications" @default.
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