In this paper, applying special properties of doubling transformation, a structure-preserving doubling algorithm is developed for computing the positive definite solutions for a nonlinear matrix ...equation. Further, by mathematical induction, we establish the convergence theory of the structure-preserving doubling algorithm. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived algorithm.
Why are many traditional governing parties of advanced democracies in decline? One explanation relates to public perceptions about mainstream party convergence. Voters think that the centre-left and ...-right are increasingly similar and this both reduces mainstream partisan loyalties and makes room for more radical challengers. Replicating and extending earlier studies, we provide evidence supporting this view. First, observational analysis of large cross-national surveys shows that people who place major parties closer together ideologically are less likely to be mainstream partisans, even when holding constant their own ideological proximity to their party. Second, a survey experiment in Germany suggests that this relationship is causal: exposure to information about policy convergence makes mainstream partisan attachments weaker. Importantly, we advance previous discussions of the convergence theory by showing that, in both our studies, ideological depolarisation is most detrimental to mainstream centre-left partisan attachments. We suggest that this is due to differing party histories.
We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/ storage is burdensome. In order to efficiently solve such ...problems, we propose a new class of algorithms which are ``derivative-free'' both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches.
The dominant narrative of global income inequality is one of convergence. Recent high-profile publications by Branko Milanovic and the World Bank claim that the global Gini coefficient has declined ...since 1988, and that inter-country inequality has declined since 1960. But the convergence narrative relies on a misleading presentation of the data. It obscures the fact that convergence is driven mostly by China; it fails to acknowledge rising absolute inequality; and it ignores divergence between geopolitical regions. This paper suggests alternative measures that bring geopolitics back in by looking at the gap between the core and periphery of the world system. From this perspective, global inequality has tripled since 1960.
In this article, an online unified solution based on stochastic configuration network (SCN) and Levenberg- Marquardt (LM) algorithm is proposed to generate optimal switching angles for selective ...harmonic elimination (SHE) in both the symmetric and asymmetric cascaded H-bridge (CHB) multilevel inverters (MLIs). Different from the traditional neural network framework for SHE, this unified solution uses SCN to only generate initial values of the switching angles online, which significantly reduce the precision demand on training SCN and avoids the local optima problem of gradient descent algorithm. After obtaining the initial values from SCN online, the LM algorithm can be used to rapidly solve the exact switching angles for SHE, which guarantees the solving efficiency and precision of the final solutions. Moreover, the stability of the proposed method is proved via Newton-like convergence theory. Compared with intelligent search algorithms and look-up table method, the proposed solution can not only online generate optimal theoretical switching angles but with much fewer data storage space. Experimental results of both symmetric and asymmetric MLI cases are presented to validate the correctness and online applicability of the proposed solution.
In this paper, we use the non-negative discrete semimartingale convergence theorems to study the stochastic theta methods with random stepsizes to reproduce the almost sure stability of the exact ...solution of stochastic differential equations. Moreover, the choice of the stepsize in each step is based on the stochastic theta methods of random variable stepsize. In numerical experiments, we propose an algorithm that successfully use θ-Maruyama and θ-Milstein methods to simulate the numerical solutions of stochastic differential equations, reproduce the almost sure stability of exact solutions of SDEs and simulate the random variable stepsize in each timestep, and compared with constant stepsizes, random stepsize can speed up the decay process and reduce the iterations greatly.
Using hierarchical age–period–cohort growth curve models, this study assesses changes in gender disparities in housework time across Chinese adults’ life course and across different birth cohorts. ...The results revealed three key findings. First, inconsistent with convergence theory, the Chinese family is still a male-dominated but male-absent family, with women still doing the majority of domestic work and showing no signs of decline with age. Second, as they age, Chinese women and men present diverging tendencies toward time spent on housework: Women tend to dedicate more time to it, and men less, resulting in a widening gender gap in housework with age. Third, although recent cohorts present lower levels of housework time than previous cohorts, this is because men from recent cohorts are doing less housework, while their female counterparts are doing almost as much as women from earlier cohorts.
An efficient single-step iteration method is presented for solving the large sparse non-Hermitian positive definite linear systems. We theoretically prove that this method converges to the unique ...solution of the system of linear equations under suitable restrictions. Moreover, we derive an upper bound for the spectral radius of the new iteration matrix. Furthermore, we consider acceleration of the new iteration by Krylov subspace methods and some special properties of the new preconditioned matrix are proposed. Numerical experiments on a few model problems are presented to further examine the effectiveness of our new method.
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