The performance of six variants of the successive overrelaxation methods (SOR) are considered for an algebraic system arising from a finite difference treatment of an elliptic equation of Partial Differential Equations (PDEs) on a triangular region. The consistency of the finite difference representation of the system is achieved. In the finite difference method one obtains an algebraic system ...

We consider the application of semi-iterative methods (SIM) to the standard (SOR) method with complex relaxation parameter ω, under the following two assumptions: (1) the associated Jacobi matrix J is consistently ordered and weakly cyclic of index 2, and (2) the spectrum σ(J ) of J belongs to a compact subset of the complex plane C, which is symmetric with respect to the origin. By using resul...

Higher order discretizations have not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to highly tuned lower order methods, such as finite-volume schemes. In this paper we investigate efficient Spectral Difference discretization...

This paper presents several new distributed algorithms to solve consensus based estimation problems in a decentralized way by adopting the well-known relaxation methods Jacobi, Gauss-Seidel and successive over-relaxation within a sensor network. In distributed estimation, all nodes collaborate to estimate the signals emitted from some common sources, employing iterative processing with one-hop ...

We study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. We prove an approximation guarantee of (1.8 + ) relative to an SDP relaxation, which matches the combinatorial approximation guarantee of Even, Feldman, Kortsarz and Nutov in ACM TALG (2009), where > 0 is a constant. We generalize the combinatorial analysis of integral solutions of Even, et al., to...

Constrained reinforcement learning (CRL), also termed as safe learning, is a promising technique enabling the deployment of RL agent in real-world systems. In this paper, we propose successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve general CRL problem, which formulated constrained Markov decision process (CMDP) context average cost. The SCAOPO on solving ...

Abstract: The parametric interpolators of modern CNC machines use Taylor’s series approximation to generate successive parameter values for the calculation of x, y, z coordinates of tool positions. In order to achieve greater accuracy, higher order derivatives are required at every sampling period which complicates the calculation for contours represented by NURBS curve. In addition, this metho...