Most existing works use dual decomposition and first-order methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This paper develops an alternative distributed Newtontype fast converging algorithm for solving NUM problems. By using novel matrix splitting techniques, both primal and dual updates for the Newton...

This paper presents the convergence analysis result of the discrete cosine transform-least-mean-square (DCT-LMS) adaptive "ltering algorithm which is based on a well-known interpretation of the variable stepsize algorithm. The time-varying stepsize of the DCT-LMS algorithm is implemented by the modi"ed power estimator to redistribute the spread power after the DCT. The performance analysis is c...

For Runge-Kutta methods (RKMs), linear multistep methods (LMMs) and classes of general linear methods (GLMs) much attention has been paid, in the literature, to special nonlinear stability requirements indicated by the terms total-variation-diminishing (TVD), strong stability preserving (SSP) and monotonicity. Stepsize conditions, guaranteeing these properties, were derived by Shu & Osher [J. C...

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §

Runge-Kutta and Adams methods are the most popular codes to solve numerically nonstiff ODEs. The Adams methods are useful to reduce the number of function calls, but they usually require more CPU time than the Runge-Kutta methods. In this work we develop a numerical study of a variable step length Adams implementation, which can only take preassigned step-size ratios. Our aim is the reduction o...

Discretizations and Grobman-Hartman Lemma, discretizations and the hierarchy of invariant manifolds about equilibria are considered. For one-step methods, it is proved that the linearizing conjugacy for ordinary differential equations in Grobman-Hartman Lemma is, with decreasing stepsize, the limit of the linearizing conjugacies of the discrete systems obtained via time-discretizations. Similar...