scholarly journals On convergence conditions for generalized Persidskii systems

2022 ◽  
Author(s):  
Wenjie Mei ◽  
Denis Efimov ◽  
Rosane Ushirobira ◽  
Alexander Aleksandrov
Keyword(s):  
Convergence Conditions

A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Convergence Conditions ◽  
Principal Angles ◽  
Factorization Formula ◽  
Ill Posed

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

scholarly journals An iterative algorithm for the system of split mixed equilibrium problem

2020 ◽  
Vol 53 (1) ◽  
pp. 309-324
Author(s):  
Ibrahim Karahan ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Equilibrium System ◽  
Convergence Conditions ◽  
Mixed Equilibrium Problems ◽  
Split Variational Inequality ◽  
Mixed Equilibrium ◽  
Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

scholarly journals Positive cones and convergence conditions for iterative methods based on splittings

2006 ◽  
Vol 413 (2-3) ◽  
pp. 319-326 ◽  
Author(s):  
Joan-Josep Climent ◽  
Victoria Herranz ◽  
Carmen Perea
Keyword(s):  
Iterative Methods ◽  
Convergence Conditions

Analysis of Convergence Conditions for the Variance of Indoor and Outdoor Temperature Differences of In-site Thermal Resistance by Average Method

2021 ◽  
Vol 28 (1) ◽  
pp. 95-102
Author(s):  
Ji-Hoon Moon ◽  
Ye-Ji Lee ◽  
Myeong-Jin Ko ◽  
Doo-Sung Choi ◽  
Yong-Shik Kim
Keyword(s):  
Thermal Resistance ◽  
Average Method ◽  
Outdoor Temperature ◽  
Convergence Conditions ◽  
Indoor And Outdoor

scholarly journals Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations

2003 ◽  
Vol 6 ◽  
pp. 297-313 ◽  
Author(s):  
Desmond J. Higham ◽  
Xuerong Mao ◽  
Andrew M. Stuart
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Finite Time ◽  
Mean Square ◽  
Convergence Conditions ◽  
Finite Time Convergence ◽  
Mean Square Stability ◽  
Exponential Mean Square Stability ◽  
Positive Results

AbstractPositive results are proved here about the ability of numerical simulations to reproduce the exponential mean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step sizes) are shown to be equivalent, and the corresponding second-moment Lyapunov exponent bounds can be taken to be arbitrarily close. The required finite-time convergence conditions hold for the class of stochastic theta methods on globally Lipschitz problems. It is then shown that exponential mean-square stability for non-globally Lipschitz SDEs is not inherited, in general, by numerical methods. However, for a class of SDEs that satisfy a one-sided Lipschitz condition, positive results are obtained for two implicit methods. These results highlight the fact that for long-time simulation on nonlinear SDEs, the choice of numerical method can be crucial.

Convergence conditions of stochastic programming algorithms

Cybernetics ◽  
1975 ◽  
Vol 9 (3) ◽  
pp. 464-468 ◽  
Author(s):  
E. A. Nurminskii
Keyword(s):  
Stochastic Programming ◽  
Convergence Conditions ◽  
Programming Algorithms

scholarly journals Convergence Conditions of Mixed States and their von Neumann Entropy in Continuous Quantum Measurements

2014 ◽  
Vol 21 (04) ◽  
pp. 1450010
Author(s):  
Toru Fuda
Keyword(s):  
Quantum Measurements ◽  
Von Neumann Entropy ◽  
Projection Operators ◽  
Mixed States ◽  
Convergence Conditions ◽  
Von Neumann ◽  
Zeno Effect ◽  
The Difference ◽  
Arbitrary Precision ◽  
Continuous Quantum Measurements

By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described as an application. In the case of an infinite dimension, although the von Neumann entropy is not necessarily continuous, the difference of the entropies between the states, as mentioned above, can be made arbitrarily small under some conditions.

Convergence conditions on the first derivative of the operator

2017 ◽  
pp. 127-159
Author(s):  
José Antonio Ezquerro Fernández ◽  
Miguel Ángel Hernández Verón
Keyword(s):  
Convergence Conditions ◽  
First Derivative

Generalization of the twisting convergence conditions to non-affine systems

Automatica ◽  
2021 ◽  
pp. 110019
Author(s):  
Dominique Monnet ◽  
Alexandre Goldsztejn ◽  
Franck Plestan
Keyword(s):  
Convergence Conditions ◽  
Affine Systems
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