This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...

We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (\read-k" monotone CNF). Let f : f0;1g n ! f0;1g be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) DNF descriptions of f. The alg...

A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation reformulated as zero finding a mixed-monotone relation, that is, difference two maximally monotone relations. problem can then be solved efficiently by borrowing existing algorithms minimize convex functions. potential illustrated on classical Van der Pol oscillator.

The theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi-type SIS epidemic model to obtain the spreading speed c∗, and the nonexistence of traveling waves with wave speed c < c∗. Then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease-free and endemic equilibria ...

&lt;p style='text-indent:20px;'&gt;Using the concept of Bregman divergence, we propose a new subgradient extragradient method for approximating common solution pseudo-monotone and Lipschitz continuous variational inequalities fixed point problem in real Hilbert spaces. The algorithm uses self-adjustment rule selecting stepsize each iteration also, prove strong convergence result sequence genera...

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. The time discretization is performed by several classes of Runge-Kutta methods (strongly A−stable or explicit stabilized methods). We discuss...

Both the bottleneck counting argument 7, 8] and Razborov's approximation method 1, 4, 12] have been used to prove exponential lower bounds for monotone circuits. We show that under the monotone circuit model for every proof by the approximation method, there is a bottleneck counting proof and vice versa. We also illustrate the elegance of the bottleneck counting technique with a simple self-exp...