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In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

Recently, Chen and Ma [A generalized shift-splitting preconditioner for complex symmetric linear systems, J. Comput. Appl. Math., 344 (2018), pp. 691–700] have presented the generalized shift-splitting (GSS) method to solve complex symmetric linear systems. In this paper, we establish a class of modified GSS (MGSS) method to extend the existing GSS method. We prove the convergence of the proposed method under suitable restrictions on the iteration parameters. Lastly, numerical experiments are carried out, and experimental results show that the new iteration method is feasible and effective. [ABSTRACT FROM AUTHOR]

The wavelet method based on the Meyer wavelet function and scaling function is a rather effective regularization method for solving some illposed problems. Recently, there are many works on this method limited to the a priori choice rule. The typical paper [H. Cheng and C.L. Fu, Wavelets and numerical pseudodifferential operator, Appl. Math. Model. 40 (2016), pp. 1776-1787] has systematically considered the a priori choice rule in the framework of the pseudodifferential operator (ψDO). In this paper, we will systematically consider the a posteriori choice rule for two kinds of ill-posed problems in the framework of the ψDO, and construct the convergence error estimates between the exact solution and its regularized approximation. [ABSTRACT FROM AUTHOR]

In this paper a singularly perturbed fourth-order ordinary differential equation is considered. The differential equation is transformed into a coupled system of singularly perturbed equations. A hybrid finite difference scheme on a Vulanović--Shishkin mesh is used to discretize the system. This hybrid difference scheme is a combination of a non-equidistant generalization of the Numerov scheme and the central difference scheme based on the relation between the local mesh widths and the perturbation parameter. We will show that the scheme is maximum-norm stable, although the difference scheme may not satisfy the maximum principle. The scheme is proved to be almost fourth-order uniformly convergent in the discrete maximum norm. Numerical results are presented for supporting the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a new conjugate gradient-based projection method for solving a system of nonlinear monotone equations is proposed. The method can be viewed as an extension of a family of conjugate gradient methods for unconstrained optimization by Li et al. [A new family of conjugate gradient methods for unconstrained optimization, J. Appl. Math. Comput. 58 (2018), pp. 219–234]. The proposed method is derivative-free which makes it suitable for large-scale nonlinear monotone equations. We show that the method satisfies the descent condition independent of line searches and that the method is globally convergent. Numerical results indicate that the proposed method is efficient. [ABSTRACT FROM AUTHOR]

In this paper, we present two nonmonotone versions of adaptive cubic regularized (ARC) method for unconstrained optimization problems. The proposed methods are a combination of the ARC algorithm with the nonmonotone line search methods introduced by Zhang and Hager [A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14 (2004), pp. 1043–1056] and Ahookhosh et al. [A nonmonotone trust-region line search method for large-scale unconstrained optimization, Appl. Math. Model. 36 (2012), pp. 478–487]. The global convergence analysis for these iterative algorithms is established under suitable conditions. Several numerical examples are given to illustrate the efficiency and robustness of the newly suggested methods. The obtained results show the satisfactory performance of the proposed algorithms when compared to the basic ARC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the convergence for improved multi-point Chebyshev-like methods is considered. Compared to the results of Chebyshev method with second derivative in reference [M.A. Hernández, M.A. Salanova, J. Comput. Appl. Math. 126 (2000), pp. 131–143], the R-order is maximised and the Hölder continuity condition is also relaxed. Moreover, these improved methods do not need second derivatives, when the computation of second derivative is large, these improved methods will be more efficient than Chebyshev method. Under the relaxed condition, an existence-uniqueness theorem is proved. The R-order of convergence for these improved methods is also analysed. [ABSTRACT FROM AUTHOR]

The 0–1 test for chaos is increasingly used in applications where it is important to distinguish between chaotic and regular dynamics of the deterministic dynamical system. This test consists of translating the time series into (p , q) plane. Then the boundedness of the object created in the (p , q) plane is inspected by computing mean square displacement and its growth rate. The computation of the mean square displacement for various lag has high computational complexity. In this paper, the inspection of the boundedness using bounding box and centre of gravity is proposed. This method has linear computational complexity and provides more control over the precision of the test through multiple input parameters. [ABSTRACT FROM AUTHOR]

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods are widely used for solving unconstrained optimization and nonlinear equations, specially in large-scale cases. Since they own the attractive practical factors of simple computation and low memory requirement, interesting theoretical features of curvature information and strong global convergence. In this paper, we present a modified conjugate gradient algorithm by line search method with acceleration scheme for nonlinear symmetric equations. Furthermore, the proposed method not only possess descent property but also owns global convergence in mild conditions. Numerical results also indicate that the presented method is much more effective than the other methods for the test problems. [ABSTRACT FROM PUBLISHER]

In this paper, a multiple-time-step decoupled algorithm for a non-stationary Stokes–Darcy problem is proposed and investigated. Under a modest time step restriction of physical parameters and the time step proportion, we give the stability analysis and convergence analysis of the decoupled scheme with different time step in fluid and porous subregions. Finally, a series of numerical experiments are provided to illustrate the accuracy, efficiency, and stability of the presented method for the coupled problem with the Beavers–Joseph–Saffman–Jones interface conditions. [ABSTRACT FROM PUBLISHER]

LetAbe a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equationAXA=XAX. We first obtain a simplified matrix equation of the same type withAreplaced by its Jordan form, whose Jordan blocks are at most. Then we obtain a system of matrix equations of smaller sizes to find all the commuting solutions of the original matrix equation. [ABSTRACT FROM PUBLISHER]

Augmentedk-aryn-cubeis proposed as a new interconnection network model by Xiang and Steward [Augmented k-ary n-cubes, Inform. Sci. 181(1) (2011), pp. 239–256]. For a connected graphG, an edge-cut (vertex-cut)Sis called a restricted edge-cut (restricted vertex-cut) ifG–Scontains no isolated vertices. The restricted edge-connectivity (restricted connectivity) ofG, denoted by(), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) ofG. In this paper, we completely determine the restricted (edge-)connectivity of. Precisely,for;for,for,forand, butdoes not have restricted vertex-cut. [ABSTRACT FROM AUTHOR]

This work is devoted to studying the problem of approximating a given matrix by the product of two low-rank structured matrix which arises in the material processing. Firstly, we analyse some properties of the original problem and utilize the alternating least squares method to reformulate it into two subproblems. Then by using the Gramian representation and a Vandermonde-like transformation, the feasible sets of the subproblems are characterized, which makes them be respectively transformed into two unconstrained minimization problems. Finally, we derive the expressions of the gradients of the objective functions and apply the gradient descent algorithm to solve them. Numerical examples are tested to show that our method performs well in terms of the residual error of the objective function. [ABSTRACT FROM PUBLISHER]

Recently, Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a finite difference scheme to solve a quasilinear fractal mobile/immobile transport model based on the new fractional derivative is introduced and analysed. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. Some a priori estimates of discreteerrors with optimal order of convergenceare established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis. [ABSTRACT FROM PUBLISHER]