We propose an approach to solving two-dimensional linear and nonlinear boundary-value problems of statics for shallow shells based on the generalized method finite integral transformations Newton– Kantorovich–Raphson linearization. In case, application is reduced construction two with respect different variables in analyzed domain under assumption that kernels one transformation are transforms ...

We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of th...

We investigate an iterative method for the solution of time-periodic parabolic PDE constrained optimization problems. It is an inexact Sequential Quadratic Programming (iSQP) method based on the Newton-Picard approach. We present and analyze a linear quadratic model problem and prove optimal mesh-independent convergence rates. Additionally, we propose a two-grid variant of the Newton-Picard met...

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

Traditionally, a regional dispatch center uses the equivalent method to deal with external grids, which fails to reflect the interactions among regions. This paper proposes a distributed N-1 contingency analysis (DCA) solution, where dispatch centers join a coordinated computation using their private data and computing resources. A distributed screening method is presented to determine the Crit...

In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step in which well-known Gauss quadrature rule is corrector step and generalized Newton taken as predictor step. The convergence of proposed established under some acceptable conditions. Numerical examples prove consistency capability new method.

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Tensor computations are increasingly prevalent numerical techniques in data science, but pose unique challenges for high-performance implementation. We provide novel algorithms and systems infrastructure which enable efficient parallel implementation of tensor completion with generalized loss functions. Specifically, we consider alternating minimization, coordinate a quasi-Newton (generalized G...

Inverse problems arise whenever one searches for unknown causes based on observation of their effects. Such problems are usually ill-posed in the sense that their solutions do not depend continuously on the data. In practical applications, one never has the exact data; instead only noisy data are available due to errors in the measurements. Thus, the development of stable methods for solving in...

A generalized least-square method with Tikonov–Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy ͑CDBS͒ spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization par...