When powerful machines such as the Cray-2 became available in the late 1980s, a number of researchers investiWe investigate the use of an inexact Newton’s method to solve the potential equations in the transonic regime. As a test case, gated use of exact Newton’s method for solving steady we solve the two-dimensional steady transonic small disturbance state CFD problems. Direct sparse matrix so...

We propose and study the iteration-complexity of a proximal-Newton method for finding approximate solutions of the problem of minimizing a twice continuously differentiable convex function on a (possibly infinite dimensional) Hilbert space. We prove global convergence rates for obtaining approximate solutions in terms of function/gradient values. Our main results follow from an iteration-comple...

For numerical optimization of the cost function of the maximum likelihood (ML) algorithm for angle-of-arrival (AOA) estimation, Newton-type method has been widely employed. In this paper, we apply the Newton-type method to the optimization of cost function for spectrum estimation-based AOA estimation algorithm of the conventional beamforming, the Capon beamfomring and the MUSIC algorithm. Expli...

The Josephy-Newton method for solving a nonlinear complementarity problem consists of solving, possibly inexactly, a sequence of linear complementarity problems. Under appropriate regularity assumptions, this method is known to be locally (superlinearly) convergent. To enlarge the domain of convergence of the Newton method, some globalization strategy based on a chosen merit function is typical...

Nf (z) = expz(−Df(z)f(z)) where expz : TzMn → Mn denotes the exponential map. When, instead of a mapping we consider a vector field X, in order to define Newton method, we resort to an object studied in differential geometry; namely, the covariant derivative of vector fields denoted here by DX. We let NX(z) = expz(−DX(z)X(z)). These definitions coincide with the usual one when Mn = Rn because e...

We propose a fully distributed Newton-type algorithm for state estimation of electric power systems. At each Newton iteration, matrix-splitting techniques are utilized to carry out the matrix inversion for calculating the Newton step in a distributed fashion. In order to reduce the communication burden as well as increase robustness of state estimation, the proposed distributed scheme relies on...

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton’s iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufftcient conditions-of purely combinatorial...

Pseudo-transient continuation is a Newton-like iterative method for computing steady-state solutions of differential equations in cases where the initial data is far from a steady state. The iteration mimics a temporal integration scheme, with the time step being increased as steady state is approached. The iteration is an inexact Newton iteration in the terminal phase. In this paper we show ho...

The long-term dynamics of many dynamical systems evolves on a low-dimensional, attracting, invariant slow manifold, which can be parameterized by only a few variables (“observables”). The explicit derivation of such a slow manifold (and thus, the reduction of the long-term system dynamics) can be extremely difficult, or practically impossible. For this class of problems, the equation-free compu...

A general outer iteration, based upon linearization, is introduced at discrete time steps for the one-dimensional semiconductor device model. The iteration depends upon solving the semidiscrete device equations approximately, specifically, in such a way that the residual is of order ∆t in an appropriate norm. It is shown that this maintains the order of the backward Euler method. A monitoring o...