scholarly journals On the construction of convergent iterative sequences of polynomials

1989 ◽  
Vol 47 (3) ◽  
pp. 382-390
Author(s):  
Qiu Weiyuan
Keyword(s):  
Initial Point ◽  
Arbitrary Initial Point

AbstractWe answer two conjectures suggested by Zalman Rubinstein. We prove his Conjecture 1, that is, we construct convergent iterative sequences for with an arbitrary initial point, where with m ≥ 2. We also show by several counterexamples that Rubinstein's Conjecture 2 is generally false.

On perturbation range in the feedback synthesis problem for a chain of integrators system

2020 ◽  
Author(s):  
V I Korobov ◽  
T V Revina
Keyword(s):  
Finite Time ◽  
Initial Point ◽  
Settling Time ◽  
Time Function ◽  
Synthesis Problem ◽  
Total Derivative ◽  
Perturbed System ◽  
Arbitrary Initial Point ◽  
Feedback Synthesis ◽  
A Chain

Abstract The feedback synthesis problem for a chain of integrators system with continuous bounded unknown perturbation is considered. Our approach is based on the controllability function (CF) method proposed by V.I. Korobov. The perturbation range is determined by the negativity condition for the total derivative of the CF with respect to the perturbed system. The control that does not depend on perturbation under some restrictions and steers an arbitrary initial point from a neighborhood of the origin to the origin in a finite time (settling-time function) is constructed. The settling-time function depends on the perturbation, but it remains bounded from below and from above by the same value.

scholarly journals Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Nonlinear Operator ◽  
Real Hilbert Space ◽  
Initial Point ◽  
Nonempty Closed Convex Subset ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Hybrid Steepest Descent Method ◽  
Arbitrary Initial Point ◽  
Mann’S Iteration ◽  
Fixed Point Sets

Assume thatFis a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subsetCof a real Hilbert spaceH. Assume also thatΩis the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings onC. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbationF, which generates two sequences from an arbitrary initial pointx0∈H. These two sequences are shown to converge in norm to the same pointPΩx0under very mild assumptions.

Automatic Operation of a Mobile Robot Using an RCE Network

1990 ◽  
Vol 2 (4) ◽  
pp. 303-307
Author(s):  
Hisato Kobayashi ◽  
◽  
Katsuhiko Inagaki
Keyword(s):  
Neural Network ◽  
Pattern Recognition ◽  
Mobile Robot ◽  
Initial Point ◽  
Coulomb Energy ◽  
Neural Net ◽  
Automatic Operation ◽  
Characteristic Equations ◽  
Arbitrary Initial Point ◽  
Energy Network

This article describes an example using a neural net as a method of mobile robot operation. The method eliminates the need for characteristic equations of a mobile robot, but requires an exercise to some extent using adequate ""patterns."" For accumulating experience of this practice, an RCE (restricted coulomb energy) network, or a pattern recognition-use neural network, is used. A simulation is conducted by driving a car into a garage. A man drives a car into a garage to create pattern data, which an RCE net is made to learn. After learning to some extent, it is allowed to put a car into a garage from an arbitrary initial point. The following are the descriptions of the results.

Dynamical cascade models for Kolmogorov's inertial flow

1980 ◽  
Vol 101 (2) ◽  
pp. 349-376 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Initial Point ◽  
Random Motion ◽  
Cascade Model ◽  
Cascade Process ◽  
Equilibrium Solutions ◽  
Cascade System ◽  
Cascade Models ◽  
Inertial Flow ◽  
The Mean ◽  
Arbitrary Initial Point

To resolve possible fluctuations about the mean motion of the Desnyansky-Novikov model for Kolmogorov's inertial flow, we have investigated two dynamical systems of the cascade process which are formally derivable from Burgers’ equation. The first cascade model produced no fluctuations, for its trajectory was identical with the Desnyansky–Novikov model's. Disappointingly, the second cascade system, which is similar to the Kerr–Siggia model, has also proved unable to engender fluctuations. This is because the second model when truncated consistently maps an arbitrary initial point into the attainable phase space of the first cascade model. However, when truncated inconsistently the trajectory of second model can exhibit a quite erratic and somewhat sporadic motion, thereby reflecting the apparently random motion of inviscid equilibrium solutions. Therefore, the observation of temporally intermittent fluctuations by a stationary Kerr–Siggia model is due to the inconsistent truncation produced by restricting energy dissipation for all but the upper truncation mode in their model.

scholarly journals A globally convergent method for finding zeros of integer functions of finite order

2017 ◽  
pp. 115-128
Author(s):  
А.Н. Громов
Keyword(s):  
Finite Order ◽  
Logarithmic Derivative ◽  
Initial Point ◽  
Globally Convergent ◽  
Finite Set ◽  
Minimum Number ◽  
Convergent Method ◽  
Arbitrary Initial Point ◽  
Partial Fractions ◽  
Derivatives Of

Предложен метод отыскания нулей целых функций конечного порядка, который сходится к корню от произвольной начальной точки, т.е. является глобально сходящимся. Метод основан на представлении производных высшего порядка от логарифмической производной в виде суммы простейших дробей и сводит отыскание корня к выбору минимального числа из конечного множества. Даны оценки скорости сходимости. A method for finding zeros of integer functions of finite order is proposed. This method converges to a root starting from an arbitrary initial point and, hence, is globally convergent. The method is based on a representation of higher-order derivatives of the logarithmic derivative as a sum of partial fractions and reduces the finding of a root to the choice of the minimum number from a finite set. The rate of convergence is estimated.

scholarly journals A variational method for the construction of convergent iterative sequences

1986 ◽  
Vol 41 (1) ◽  
pp. 51-58 ◽  
Author(s):  
Zalman Rubinstein
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Analytic Function ◽  
Variational Method ◽  
Connected Domain ◽  
Initial Point ◽  
Proper Subset ◽  
Simply Connected Domain ◽  
Arbitrary Initial Point ◽  
Simply Connected

AbstractConvergent iterative sequences are constructed for the polynomials fm = z + zm, m ≧ 2, with initial point the lemniscate {z: |fm (z)| ≦1}. In the particular case m = 2 convergent iterative sequences are constructed also for f-1m, (z) with an arbitrary initial point. The method is based on a certain variational principle which allows reducing the problem to the well known situation of an analytic function mapping a simply connected domain into a proper subset of itself and possessing a fixed point in the domain.

scholarly journals Weak and strong convergence of an iterative method for nonexpansive mappings in Hilbert spaces

2008 ◽  
Vol 2 (2) ◽  
pp. 197-204 ◽  
Author(s):  
Yu Miao ◽  
Li Junfen
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Iterative Process ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Initial Point ◽  
Lipschitzian Mapping ◽  
Weak And Strong Convergence ◽  
Convergence Results ◽  
Arbitrary Initial Point

In a real Hilbert space H, starting from an arbitrary initial point x0 H, an iterative process is defined as follows: xn+1 = anxn +(1-an)T?n+1 f yn, yn = bnxn + (1 - bn)T?n g xn, n ? 0, where T ?n+1 f x = Tx - ?n+1?f f(Tx), T?n g x = Tx - ?n?gg(Tx), (8 x 2 H), T : H ? H a nonexpansive mapping with F(T) 6= ; and f (resp. g) : H ? H an ?f (resp. ?g)-strongly monotone and kf (resp. kg)-Lipschitzian mapping, {an} _ (0, 1), {bn} _ (0, 1) and {?n} _ [0, 1), {?n} _ [0, 1). Under some suitable conditions, several convergence results of the sequence {xn} are shown.

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