The t-value of a (t,m, s)-net is an important criterion of point sets for quasiMonte Carlo integration, and many point sets are constructed in terms of tvalues, as this leads to small integration error bounds. Recently, Matsumoto, Saito, and Matoba proposed the Walsh figure of merit (WAFOM) as a quickly computable criterion of point sets that ensure higher order convergence for function classes...

Alternating direction method of multipliers (ADMM) has been widely used in many applications due to its promising performance to solve complex regularization problems and large-scale distributed optimization problems. Stochastic ADMM, which visits only one sample or a mini-batch of samples each time, has recently been proved to achieve better performance than batch ADMM. However, most stochasti...

This paper gives a general convergence analysis to the truncated incomplete Hessian Newton method (T-IHN). It shows that T-IHN is globally convergent even with an indefinite incomplete Hessian matrix or an indefinite preconditioner, which may happen in practice. It also proves that when the T-IHN iterates are close enough to a minimum point, T-IHN has a Q-linear rate of convergence, and an admi...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

in this paper, economic convergence in selected oic (36 countries) is studied. the convergence hypothesis is tested through three approaches: beta convergence, sigma convergence, and time series model. ols is used for estimating the cross section model and cross variance is used to test the distributive model. for analyzing time series model, we used augmented dicky fuller test. beta convergenc...

The behavior of difference approximations of hyperbolic partial differential equations as time t -* oo is studied. The rate of convergence to steady state is analyzed theoretically and expe ¡mentally for the advection equation and the linearized Euler equations. The choice of difference formulas and boundary conditions strongly influences the rate of convergence in practical steady state calcul...

Nonlinear versions of the Lie-Trotter product formula exp[t(A + B)] = \im„^x[exp((t/n)A)exp((t/n)B)}" and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations. 0. Introduction. The Lie-Trotter product formula states that (0.1) exp(^)exp(^)exp(^C e,(A + B+c) asn^oo. (The exponent n indicates itera...

With a weighting scheme proportional to t, a traditional stochastic gradient descent (SGD) algorithm achieves a high probability convergence rate of O(κ/T ) for strongly convex functions, instead of O(κ ln(T )/T ). We also prove that an accelerated SGD algorithm also achieves a rate of O(κ/T ).

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...