A complex system of linear equations arises in many important applications. We further explore algebraic and convergence properties and present analytical and numerical comparisons among several ...available iteration methods such as C-to-R and PMHSS for solving such a class of linear systems. Theoretical analyses and computational results show that reformulating a complex linear system into an equivalent real form is a feasible and effective approach, for which we can construct, analyze, and implement accurate, efficient, and robust preconditioned iteration methods.
A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial ...differential equations. The algorithms in this class make use of the discretization level as a means of speeding up the computation of the step. This use is recursive, leading to true multilevel/multiscale optimization methods reminiscent of multigrid methods in linear algebra and the solution of partial differential equations. A simple algorithm of the class is then described and its numerical performance is shown to be numerically promising. This observation then motivates a proof of global convergence to first-order stationary points on the fine grid that is valid for all algorithms in the class.
It is well known that many popular variational, quasi-variational, hemivariational inequalities and variational inclusions involving constraints in a Banach space to convert a fixed point problems ...for finding the solution of such problems. This paper is to infuse a sequence of penalized problems without constraints and we show under the few reasonable assumptions to the Kuratowski upper limit with respect to the weak topology of the sets of solutions to penalized problems is nonempty. As an application, we explore two complicated partial differential systems of elliptic mixed boundary value problem involving a nonlinear nonhomogeneous differential operator with an obstacle effect, and a nonlinear elastic contact problem in mechanics with unilateral constraints.
In this paper, we introduce a class of SOR-like iteration methods for solving the systems of the weakly nonlinear equation, which is by reformulating equivalently the weakly nonlinear equation as a ...two-by-two block nonlinear equation. Two types of the global convergence theorems are given under suitable choices of the involved splitting matrix and parameter. Numerical results for the three-dimensional nonlinear convection-diffusion equation and the linear complementarity problem show that the proposed iteration methods are feasible and efficient for solving the weakly nonlinear equations.
This paper represents a “studying‐up” of the controversy over federal regulatory processes regarding protection of Lakota and Dakota cultural heritage in permitting the Dakota Access Pipeline (DAPL). ...To analyse this controversy, I engage with interest‐convergence theory, a component of Critical Race Theory, alongside a critique of its arguably simplistic definition of “white interests.” Agreeing that we need a finer‐grained understanding of elite interests as multiple, conflicting, and not always based purely in material self‐interest, I argue that interests should be understood as nonhuman components of elite assemblages, shaped by both emotions and societal ideologies yet constrained by – and in conflict with – top‐down, ideology‐driven missions and institutional cultural norms, as well as pressure from other assemblages. I use this framework to examine conflicts within and among various elite assemblages’ interests surrounding Lakota and Dakota cultural heritage. The US Army Corps of Engineers’ emotion‐ and ideology‐driven interests in demonstrating sensitivity to tribes’ concerns were constrained by their mission‐driven interests in accomplishing duties in a timely manner. These interests, in turn, conflicted with concerns (or lack thereof) manifested by other federal entities (Advisory Council on Historic Preservation, DC District Court) about DAPL’s impacts on cultural heritage, and with the company’s and federal government’s financial interests in pressuring USACE to enable completion of the pipeline’s construction. I unpack power differentials and dynamics among these various groups, as realised through particular interpretations and implementations of relevant legislation. I suggest that examining such “conflicts of interests” within and between elite assemblages, within the legal production of space, can elucidate controversies over industrial expansion’s socio‐environmental threats.
This paper represents a “studying‐up” of the controversy over federal regulatory processes regarding protection of Lakota and Dakota cultural heritage in permitting the Dakota Access Pipeline (DAPL). I argue that interests should be understood as components of elite assemblages, shaped by both emotions and societal ideologies yet constrained by – and in conflict with – top‐down, ideology‐driven missions and institutional cultural norms, as well as pressure from other assemblages. I use this framework to examine conflicts within and among various elite assemblages’ interests surrounding Lakota and Dakota cultural heritage, and suggest that examining such “conflicts of interests” within and between elite assemblages, within the legal production of space, can elucidate controversies over industrial expansion’s socio‐environmental threats.
In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to ...implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.
Bangladesh’s remarkable achievements in economic and social progress have placed the country in a position that was unimaginable just 20 years ago. However, has such improvement in development ...outcomes been equal across all areas within the country? We aim to address this question by analyzing district-level income per capita derived from the 2000 and 2016 rounds of the Household Income and Expenditure Survey. Using models based on standard neoclassical economic convergence theory, which may also account for natural disasters, we find little evidence of convergence. This suggests that income differentials among Bangladesh’s 64 districts persist. We also examined the possibility of multiple steady states by estimating models with a three-club structure based on income percentiles as registered in 2000. However, we found no evidence of conditional convergence. Additionally, we explored the potential for endogenous club formation using regression trees and machine learning algorithms. Yet, once again, the results did not support convergence. Overall, our findings reveal no evidence of conditional convergence in income among Bangladesh’s districts. This implies that policy implications might vary, with targeted interventions possibly necessary to address the specific factors hindering convergence among similar regions.
This study addresses practical stability and stabilisation of switched delay systems with bounded non-vanishing perturbations. By introducing a new method, i.e. the convergence theory of the ...geometric series, several stability and stabilisation criteria are derived under the average dwell switching. An example is also given to illustrate the effectiveness of the theoretical results.
By further generalizing the modified skew-Hermitian triangular splitting iteration methods studied in L. Wang, Z.-Z. Bai, Skew-Hermitian triangular splitting iteration methods for non-Hermitian ...positive definite linear systems of strong skew-Hermitian parts, BIT Numer. Math. 44 (2004) 363–386, in this paper, we present a new iteration scheme, called the product-type skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this method. Moreover, when it is applied to precondition the Krylov subspace methods, the preconditioning property of the product-type skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that the product-type skew-Hermitian triangular splitting iteration method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts.
We address the solution of constrained nonlinear systems by new linesearch quasi-Newton methods. These methods are based on a proper use of the projection map onto the convex constraint set and on a ...derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.
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