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A large family of paradigmatic models arising in the area of image/signal processing, machine learning and statistics regression can be boiled down to consensus optimization. This paper is devoted to a class of consensus optimization by reformulating it as monotone plus skew-symmetric inclusion. We propose a distributed optimization method by deploying the algorithmic framework of generalized alternating direction implicit method. Under some mild conditions, the proposed method converges globally. Furthermore, the preconditioner is exploited to expedite the efficiency of the proposed method. Numerical simulations on sparse logistic regression are implemented by variant distributed fashions. Compared to some state-of-the-art methods, the proposed method exhibits appealing numerical performances, especially when the relaxation factor approaches to zero.

We aim to find conditions on two Hilbert space operators A and B under which the expression AX-XB having low rank forces the operator X itself to admit a good low rank approximation. It is known that this can be achieved when A and B are normal and have well-separated spectra. In this paper, we relax this normality condition, using the idea of operator dilations. The basic problem then becomes the lifting of Sylvester equations, which is reminiscent of the classical commutant lifting theorem and its variations. Our approach also allows us to show that the (factored) alternating direction implicit method for solving Sylvester equations AX-XB=C can be quick, even without requiring A to be normal.

A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit method based on the Crank–Nicolson method combined with the L 1 -approximation of the time Caputo derivative of order α ∈ ( 1 , 2 ) . It is proved that this scheme is stable, and of optimal accuracy in various norms. Numerical experiments demonstrate the predicted global convergence rates and also superconvergence.

In this study, we established a wavelet method, based on Haar wavelets and finite difference scheme for two-dimensional time fractional reaction–subdiffusion equation. First by a finite difference approach, time fractional derivative which is defined in Riemann–Liouville sense is discretized. After time discretization, spatial variables are expanded to truncated Haar wavelet series, by doing so a fully discrete scheme obtained whose solution gives wavelet coefficients in wavelet series. Using these wavelet coefficients approximate solution constructed consecutively. Feasibility and accuracy of the proposed method is shown on three test problems by measuring error in \\[L_{\\infty }\\] norm. Further performance of the method is compared with other methods available in literature such as meshless-based methods and compact alternating direction implicit methods.

Purpose This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport. Design/methodology/approach The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated. Findings Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model. Research limitations/implications The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects. Practical implications The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design. Originality/value A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

The present study aims to provide a theoretical and numerical evaluation of the bioconvective flow of micropolar fluids influenced by chemical reactions and radiation effects in the presence of a porous medium. The flow is induced by a porous vibrating surface and regulated by an externally applied magnetic field. Radiative phenomena are represented by nonlinear expressions. To efficiently approximate the solution of the non-dimensional governing equations, the alternating direction implicit method, a conditionally stable and computationally efficient numerical scheme, has been employed. This study produces distinct and effective outcomes by rigorously applying the principles of micropolar fluid theory. With the aid of graphical representations, this study explores the individual effects of various key parameters inherent to the physical model, including thermal, momentum, microrotation, and concentration fields within the boundary region. The results indicate that the proposed approach is a simple yet effective tool for analyzing the solutions of this complex micro-fluid model. Furthermore, a tabular analysis clarifies the influence of relevant constraints on the skin friction coefficient at the plate. Significantly, the findings show excellent agreement with previous studies, thereby confirming the reliability of this research.

This paper is concerned with the mean curvature flow, which describes the dynamics of a hypersurface whose normal velocity is determined by local mean curvature. We present a Cartesian grid-based method for solving mean curvature flows in two and three space dimensions. The present method embeds a closed hypersurface into a fixed Cartesian grid and decomposes it into multiple overlapping subsets. For each subset, extra tangential velocities are introduced such that marker points on the hypersurface only moves along grid lines. By utilizing an alternating direction implicit (ADI)-type time integration method, the subsets are evolved alternately by solving scalar parabolic partial differential equations on planar domains. The method removes the stiffness using a semi-implicit scheme and has no high-order stability constraint on time step size. Numerical examples in two and three space dimensions are presented to validate the proposed method.

In this paper, based on the weighted alternating direction implicit method, we investigate a second-order scheme with variable steps for the two-dimensional time-fractional telegraph equation (TFTE). Firstly, we derive a coupled system of the original equation by the symmetric fractional-order reduction (SFOR) method. Then the renowned L 2- 1 σ formula on graded meshes is employed to approximate the Caputo derivative and a weighted ADI scheme for the coupled problem is constructed. In addition, with the aid of the Grönwall inequality, the unconditional stability and convergence of the weighted ADI scheme are analyzed. Finally, the numerical experiments are shown to verify the effectiveness and correctness of theoretical results.

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order . In the current work we find implicit SSP Runge–Kutta methods with high linear order p l i n ≤ 9 and nonlinear orders p = 2 , 3 , 4 , that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order p l i n ≤ 7 and nonlinear orders up to p = 4 . We also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.

Horizontal gene transfer is a fundamental driver of prokaryotic evolution, facilitating the acquisition of novel traits and adaptation to new environments. Despite its importance, methods for inferring horizontal gene transfer are rarely systematically compared, leaving a gap in our understanding of their relative strengths and limitations. Validating horizontal gene transfer inference methods is challenging due to the absence of a genomic fossil record that could confirm historical transfer events. Without an empirical gold standard, new inference methods are typically validated using simulated data; however, these simulations may not accurately capture biological complexity and often embed the same assumptions used in the inference methods themselves. Here, we leverage the tendency of horizontal gene transfer events to involve multiple neighboring genes to assess the accuracy of diverse horizontal gene transfer inference methods. We show that methods analyzing gene family presence/absence patterns across species trees consistently outperform approaches based on gene tree-species tree reconciliation. Our findings challenge the prevailing assumption that explicit phylogenetic reconciliation methods are superior to simpler implicit methods. By providing a comprehensive benchmark, we offer practical recommendations for selecting appropriate methods and indicate avenues for future methodological advancements.