This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational c...

We analyze finite volume schemes of arbitrary order r for the one-dimensional singularly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as (Nln(N + 1)), where 2N is the number of subintervals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order (Nln(N + 1)...

We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ω-continuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k ∈ N” (i.e. k = k + 1 holds) in the sense of [1]. We apply these results to (1) obtain a generalization of Par...

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting rank vectors called ordinal patterns or just permutations. The reasons for increasing popularity this in analysis include that (i) it converges to Kolmogorov-Sinai underlying dynamics limit ever longer permutations, and (ii) its computation dispenses with generating ad hoc partit...

In this paper, a fault tolerant control for induction motors based on backstepping strategy is designed. The proposed approach permits to compensate both the rotor resistance variations and the load torque disturbance. Moreover, to avoid the use of speed and flux sensors, a second order sliding mode observer is used to estimate the flux and the speed. The used observer converges in a finite tim...

In this paper, we propose a new entropy satisfying finite volume method to solve the FokkerPlanck equation of FENE dumbbell model for polymers, subject to homogeneous fluids. Both semi-discrete and fully discrete schemes satisfy all three desired properties: i) mass conservation, ii) positivity preserving, and iii) entropy satisfying. These ensure that the computed solution is a probability den...

The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. T...