Two types of low cost-per-iteration gradient descent methods have been extensively studied in parallel. One is online or stochastic gradient descent ( OGD/SGD), and the other is randomzied coordinate descent (RBCD). In this paper, we combine the two types of methods together and propose online randomized block coordinate descent (ORBCD). At each iteration, ORBCD only computes the partial gradie...

In this work, the anisotropic linear elastic properties of two-phase composite materials, made up of square inclusions embedded in a matrix, are investigated. The inclusions present a fractal hierarchical distribution and are supposed to have the same Poisson's ratio as the matrix but a different Young's modulus. The effective elastic moduli of the medium are computed at each fractal iteration ...

In this paper, application of the complexity reduction approach based on halfand quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermo...

We introduce composite iterative schemes by the viscosity iteration method for finding a zero of an accretive operator in reflexive Banach spaces. Then, under certain differen control conditions, we establish strong convergence theorems on the composite iterative schemes. The main theorems improve and develop the recent corresponding results of Aoyama et al. 2007 , Chen and Zhu 2006, 2008 , Jun...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

The accelerated proximal gradient (APG) method, first proposed by Nesterov for minimizing smooth convex functions, later extended by Beck and Teboulle to composite convex objective functions, and studied in a unifying manner by Tseng, has proven to be highly efficient in solving some classes of large scale structured convex optimization (possibly nonsmooth) problems, including nuclear norm mini...

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal...

A simulator, which includes a full three dimensional, multi-component and three phase model for secondary oil migration is used to study ow through fractured and faulted regions. A control volume discretization is used to discretize the strongly coupled system of partial diierential equations the model creates. Non-regular and non-matching local grid reenement (LGR) is used in critical areas to...