In this paper, we present SILCA-Newton-Krylov, a new method for accurate, efficient and robust timedomain VLSI circuit simulation. Similar to SPICE, SILCA-Newton-Krylov uses time-difference and Newton-Raphson for solving nonlinear differential equations from circuit simulation. But different from SPICE, SILCA-Newton-Krylov explores a preconditioned flexible generalized minimal residual (FGMRES)...

This paper presents a detailed description of the computer implementation of a generalized midpoint algorithm for integration of constitutive relations for von Mises’ hardening material. A nonlinear scalar equation for determination of the plastic multiplier is derived. The solution of this equation for a hardening material, by the Newton-Raphson method, usually converges in threefour iteration...

In [S. Bütikofer, Math. Methods Oper. Res., 68 (2008), pp. 235–256] a nonsmooth Newton method globalized with the aid of a path search was developed in an abstract framework. We refine the convergence analysis given there and adapt this algorithm to certain finite dimensional optimization problems with C1,1 data. Such problems arise, for example, in semi-infinite programming under a reduction a...

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected N...

a new approach utilizing newton method and homotopy analysis method (ham) is proposed for solving nonlinear system of equations. accelerating the rate of convergence of ham, and obtaining a global quadratic rate of convergence are the main purposes of this approach. the numerical results demonstrate the efficiency and the performance of proposed approach. the comparison with conventional homoto...

In this study, we provide suucient conditions for controllingthe residuals of perturbed Newton-like methods, in such a way that the convergence of such methods is ensured. In order to achieve this, we apply a theorem due to Kantorovich on a setting of a regular space with a convergence structure. In this study, we are concerned with approximating a solution x of the nonlinear operator equation ...

The generalized Nash equilibrium problem is a generalization of the standard Nash equilibrium problem, in which both the utility function and the strategy space of each player may depend on the strategies chosen by all other players. This problem has been used to model various problems in applications but convergent solution algorithms are extremely scare in the literature. In this article, we ...

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically com...

We present in this work a new and shorter proof of the generalized λ-Newton inequalities for elementary symmetric functions defined on a self-conjugate set which lies essentially in the open right half-plane. We also point out some interesting consequences of the generalized λ-Newton inequalities. In particular, we establish an improved complex version of the arithmetic mean-geometric mean ineq...