scholarly journals NUMERICAL ALGORITHM FOR SOLVING THE CONTINUATION PROBLEM FOR THE ACOUSTIC EQUATION

2020 ◽  
Vol 70 (2) ◽  
pp. 7-13
Author(s):  
J.A. Askerbekova ◽  
Keyword(s):  
Inverse Problem ◽  
Convergence Rate ◽  
Direct Problem ◽  
Natural Extension ◽  
Nonlinear Problems ◽  
Initial Boundary ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

In this paper we consider the initial-boundary value problem for the acoustics equation in the temporal-triangular domain. We reduce the original ill-posed problem to an equivalent inverse problem with respect to some direct problem. This direct problem is well-posed. The inverse problem is replaced by a minimization problem. An algorithm for solving the inverse problem by the Landweber iteration method is constructed. We apply the method of successive approximations to the equation, we obtain a natural extension to nonlinear problems. This method leads to optimal convergence rate in certain cases. An analysis of the iterative Landweber method for nonlinear problems depends on the source conditions and additional conditions. Convergence analysis and error estimates are usually made with many assumptions, which are very difficult to verify from a practical point of view. This method leads to optimal convergence rate under certain conditions. Theoretical analysis is confirmed by numerical results. Visual examples are processed numerically.

scholarly journals Frictional Heating During Sliding of two Semi-Spaces with Arbitrary Thermal Nonlinearity

2014 ◽  
Vol 8 (4) ◽  
pp. 204-208 ◽  
Author(s):  
Ewa Och
Keyword(s):  
Thermal Conductivity ◽  
Frictional Heating ◽  
Thermal Contact ◽  
Nonlinear Problems ◽  
Initial Boundary ◽  
Linearization Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Coefficient Of Thermal Conductivity ◽  
Kirchhoff Transformation

Abstract Analytical and numerical solution for transient thermal problems of friction were presented for semi limited bodies made from thermosensitive materials in which coefficient of thermal conductivity and specific heat arbitrarily depend on the temperature (materials with arbitrary non-linearity). With the constant power of friction assumption and imperfect thermal contact linearization of nonlinear problems formulated initial-boundary thermal conductivity, using Kirchhoff transformation is partial. In order to complete linearization, method of successive approximations was used. On the basis of obtained solutions a numerical analysis of two friction systems in which one element is constant (cermet FMC-845) and another is variable (grey iron ChNMKh or aluminum-based composite alloy AL MMC) was conducted

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

Reachability of Optimal Convergence Rate Estimates for High-Order Numerical Convex Optimization Methods

2019 ◽  
Vol 99 (1) ◽  
pp. 91-94
Author(s):  
A. V. Gasnikov ◽  
E. A. Gorbunov ◽  
D. A. Kovalev ◽  
A. A. M. Mokhammed ◽  
E. O. Chernousova
Keyword(s):  
Convex Optimization ◽  
Convergence Rate ◽  
Optimization Methods ◽  
High Order ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

Trimmed estimators for large dimensional sparse covariance matrices

2018 ◽  
Vol 08 (01) ◽  
pp. 1950003
Author(s):  
Guangren Yang ◽  
Xia Cui
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Covariance Matrices ◽  
Optimal Convergence Rate ◽  
Sample Covariance Matrices ◽  
Optimal Convergence ◽  
Sample Covariance ◽  
Starting Point ◽  
Pairwise Product

In this paper, we will propose two new estimators for sparse covariance matrix. Our starting point is to make the estimator of each element of covariance matrix more robust. More precisely, we will trim the observations for each pairwise product of components of population as a first step. Then we form the sample covariance matrices based on the trimmed data. Finally, we apply the thresholding to the derived sample covariance matrices. These two new estimators will be shown to achieve the optimal convergence rate.

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