Energy-corrected finite element methods provide an attractive technique to deal with elliptic problems in domains with re-entrant corners. Optimal convergence rates in weighted L2-norms can be fully recovered by a local modification of the stiffness matrix at the re-entrant corner, and no pollution effect occurs. Although the existence of optimal correction factors is established, it remains op...

The classical division algorithm for polynomials requires O(n) operations for inputs of size n. Using reversal technique and Newton iteration, it can be improved to O(M(n)), where M is a multiplication time. But the method requires that the degree of the modulo, x, should be the power of 2. If l is not a power of 2 and f(0) = 1, Gathen and Gerhard suggest to compute the inverse, f, modulo x r⌉,...

Nonnegative Matrix Factorization (NMF) is a technique to approximate a nonnegative matrix as a product of two smaller nonnegative matrices. The guaranteed nonnegativity of the factors allows interpreting the approximation as an additive combination of features, a distinctive property that other widely used matrix factorization methods do not have. Several advanced methods for computing this fac...

This contribution introduces an efficient methodology for the fast periodic steady state solution of nonlinear power networks. It is based on the application of the Poincaré map to extrapolate the solution to the limit cycle through a Newton method based on a Discrete Exponential Expansion (DEE) procedure. The efficiency of the proposed DEE method is demonstrated with a case study compared agai...

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0 ≤ u ≤ 1 and ∫ u = m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth Newton method. A regularization of the nonsmooth equation is necessary to obtain the superlinear co...

diamondoids are cage-like saturated hydrocarbons consisting of fused cyclohexane rings. thediamondoids family of compounds is one of the best candidates for molecular building blocks (mbbs)in nanotechnology to construct organic nanostructures compared to other mbbs known so far. thechallenge is to find a route for self-assembly of these cage hydrocarbons and their applications in thebottom-up s...

stretching process of sheet metals in both cases of axisymmetric and non-axisymmetric is analyzed. a rigid-plastic, normal anisotrop material is assumed and large strain formulation is applied. triangular elements are used and stiffness equations of elements are obtained from virtual work principle. these nonlinear equations are linearized by newton-raphsons method and are solved by gaussian el...

This paper presents a topology with a reduced number of switches, which is used to reduce the total harmonic distortion (THD%) using MCPWM technique, MCPWM with trapezoidal reference wave and also SHE technique such as PSO technique and Newton-Raphson (NR) technique. SHE technique is used to eliminate a particular harmonic in a multilevel inverter (MLI);the MCPWM and Trapezoidal reference wave ...

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 6 x ⊥ (Mx + q) > 0 can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x,Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in ...

This paper presents a new context for using the sparse Broyden update method to solve systems of nonlinear equations. The setting for this work is that a Newton-like algorithm is assumed to be available which incorporates a workable strategy for improving poor initial guesses and providing a satisfactory Jacobian matrix approximation whenever required. The total cost of obtaining each Jacobian ...