Monotone Convergence

2021 ◽  
pp. 105-132
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Monotone Convergence

scholarly journals On an Aitken-Steffensen-Newton type method

2018 ◽  
Vol 34 (1) ◽  
pp. 85-92
Author(s):  
ION PAVALOIU ◽  
Keyword(s):  
Local Convergence ◽  
Convergence Result ◽  
Convergence Order ◽  
Monotone Convergence ◽  
Type Method ◽  
Numerical Examples ◽  
Newton Iterations ◽  
Convergence Orders

We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We prove a local convergence result showing the q-convergence order 7 of the iterations. Under certain supplementary conditions, we obtain monotone convergence of the iterations, providing an alternative to the usual ball attraction theorems. Numerical examples show that this method may, in some cases, have larger (possibly sided) convergence domains than other methods with similar convergence orders.

scholarly journals On Fuzzy Henstock-Kurzweil-Stieltjes-♦-Double Integral on Time scales

2021 ◽  
Vol 2 (2) ◽  
pp. 38-49
Author(s):  
David AFARIOGUN ◽  
Adesanmi MOGBADEMU ◽  
Hallowed OLAOLUWA
Keyword(s):  
Uniform Convergence ◽  
Time Scales ◽  
Convergence Theorem ◽  
Monotone Convergence ◽  
Double Integral ◽  
Monotone Convergence Theorem ◽  
Integrable Functions ◽  
Dominated Convergence

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

scholarly journals Global monotone convergence of Newton iteration for a nonlinear eigen-problem

2002 ◽  
Vol 357 (1-3) ◽  
pp. 217-228 ◽  
Author(s):  
Y.S. Choi ◽  
I. Koltracht ◽  
P.J. McKenna ◽  
N. Savytska
Keyword(s):  
Newton Iteration ◽  
Monotone Convergence

scholarly journals On time dependent multistep dynamic processes

1991 ◽  
Vol 43 (1) ◽  
pp. 51-61
Author(s):  
Ferenc Szidarovszky ◽  
Ioannis K. Argyros
Keyword(s):  
Topological Space ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Scale ◽  
Time Dependent ◽  
Dynamic Processes ◽  
Monotone Convergence ◽  
Speed Of Convergence ◽  
Nonlinear Difference Equations ◽  
Ordered Topological Space

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.

Monotone convergence theorems for semi-bounded operators and forms with applications

2010 ◽  
Vol 140 (5) ◽  
pp. 927-951 ◽  
Author(s):  
Jussi Behrndt ◽  
Seppo Hassi ◽  
Henk de Snoo ◽  
Rudi Wietsma
Keyword(s):  
Differential Operators ◽  
Multiplication Operators ◽  
Monotone Convergence ◽  
Monotone Sequence ◽  
Bounded Operators ◽  
Von Neumann ◽  
Sturm Liouville ◽  
Adjoint Operators ◽  
Liouville Operators

AbstractLet Hn be a monotone sequence of non-negative self-adjoint operators or relations in a Hilbert space. Then there exists a self-adjoint relation H∞ such that Hn converges to H∞ in the strong resolvent sense. This result and related limit results are explored in detail and new simple proofs are presented. The corresponding statements for monotone sequences of semi-bounded closed forms are established as immediate consequences. Applications and examples, illustrating the general results, include sequences of multiplication operators, Sturm–Liouville operators with increasing potentials, forms associated with Kreĭn–Feller differential operators, singular perturbations of non-negative self-adjoint operators and the characterization of the Friedrichs and Kreĭn–von Neumann extensions of a non-negative operator or relation.

scholarly journals Extended Real-Valued Double Sequence and Its Convergence

2015 ◽  
Vol 23 (3) ◽  
pp. 253-277 ◽  
Author(s):  
Noboru Endou
Keyword(s):  
Convergence Theorem ◽  
Double Sequence ◽  
Monotone Convergence ◽  
Double Sequences ◽  
Monotone Convergence Theorem ◽  
Fatou’S Lemma ◽  
Fatou's Lemma

Abstract In this article we introduce the convergence of extended realvalued double sequences [16], [17]. It is similar to our previous articles [15], [10]. In addition, we also prove Fatou’s lemma and the monotone convergence theorem for double sequences.

scholarly journals A PD-Type Iterative Learning Control for a Class of Switched Discrete-Time Systems with Model Uncertainties and External Noises

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Xuan Yang
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Learning Control ◽  
Iterative Learning ◽  
Time Interval ◽  
Monotone Convergence ◽  
Model Uncertainties ◽  
Time Systems

A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness.

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