The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters

2021 ◽  
Author(s):  
Jie Sun ◽  
Min Zhang
Keyword(s):  
Numerical Experiment ◽  
Rate Of Convergence ◽  
Decoupling Algorithm

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

A Fast Decoupling Algorithm for Image Super-resolution Reconstruction of Space-invariant System

2010 ◽  
Vol 36 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Li-Li HUANG ◽  
Liang XIAO ◽  
Zhi-Hui WEI ◽  
Jun ZHANG
Keyword(s):  
Super Resolution ◽  
Invariant System ◽  
Image Super Resolution ◽  
Decoupling Algorithm

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

Microwave Field Distribution Uniformity Coefficient in the Grain Mass

2020 ◽  
Vol 67 (2) ◽  
pp. 87-92
Author(s):  
Dmitriy A. Budnikov
Keyword(s):  
Electromagnetic Field ◽  
Numerical Experiment ◽  
Microwave Field ◽  
Research Purpose ◽  
Coefficient Of Determination ◽  
Material Research ◽  
Dense Layer ◽  
Uniformity Coefficient ◽  
Average Value ◽  
Processed Material

The article considers the microwave electromagnetic fields as one of the options for improving the thermal drying of grain. Their application is limited by the high unevenness of the field propagation in the layer of the processed material. (Research purpose) The research purpose is in justifying the uniformity of distribution of microwave field in the layer of the processed grain. (Materials and methods) The article presents the scheme of computer models of microwave processing zones and waveguides, properties of materials for conducting a numerical experiment. (Results and discussion) A numerical experiment was performed to determine the uniformity coefficient of propagation of the microwave field in a layer of grain material. The article presents the dependencies. (Conclusions) It was found that the results of modeling the distribution of the electromagnetic field in the zone of microwave convective influence of the installation containing two sources of microwave power for processing the grain layer indicate a high level of its unevenness in the volume of the product pipeline. To assess the uniformity of the distribution of the electromagnetic field in the working area of a laboratory installation, there used a coefficient that is the ratio of the average value of the intensity in the zone of microwave convective action to its average value of the wave strength passing through the output of the waveguide. The values of the uniformity coefficient in the considered implementation options are in the range of 0.1757-0.4946 for a dense layer of wheat. To ensure a sufficient level of uniformity of the electromagnetic wave distribution in the volume of the microwave convective zone, the uniformity coefficient must be higher than 0.37. The article presents the dependence of the uniformity coefficient of the electromagnetic field on the humidity of the processed material by a third-degree polynomial with a coefficient of determination higher than 0.98.

The rate of convergence for quadratic forms

1997 ◽  
Vol 37 (3) ◽  
pp. 191-206
Author(s):  
A. Basalykas
Keyword(s):  
Rate Of Convergence ◽  
Quadratic Forms

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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.

scholarly journals Self-exciting multifractional processes

2021 ◽  
Vol 58 (1) ◽  
pp. 22-41
Author(s):  
Fabian A. Harang ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Rate Of Convergence ◽  
Existence And Uniqueness ◽  
Volterra Equation ◽  
The Self ◽  
The Past ◽  
Stochastic Volterra Equation ◽  
Multifractional Brownian Motion ◽  
Self Organizing

AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give the rate of convergence, which is dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

Sign in / Sign up

Export Citation Format

Share Document