Least-Squares and Stochastic Gradient Algorithms Have the Same Convergence Rate Order

1996 ◽  
Vol 29 (1) ◽  
pp. 5198-5203
Author(s):  
Miloje S. Radenkovic
Keyword(s):  
Convergence Rate ◽  
Least Squares ◽  
Stochastic Gradient ◽  
Gradient Algorithms

scholarly journals Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

Heliyon ◽  
2021 ◽  
pp. e07499
Author(s):  
Mahmoud Muhammad Yahaya ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal ◽  
Sani Aji
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Gradient Algorithms

scholarly journals Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
J. Amani ◽  
A. Saboor Bagherzadeh ◽  
T. Rabczuk
Keyword(s):  
Convergence Rate ◽  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Least Square ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
Shape Functions ◽  
Numerical Errors ◽  
Elasticity Problems

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

Identification of Hammerstein Systems with Two-Segment Preload Nonlinearity Based on the Gradient Search

2014 ◽  
Vol 651-653 ◽  
pp. 2314-2317 ◽  
Author(s):  
Hong Fen Zou
Keyword(s):  
Convergence Rate ◽  
Special Form ◽  
Approximation Theorem ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Gradient Search ◽  
Unknown Parameters ◽  
Hammerstein System ◽  
Hammerstein Systems ◽  
Stochastic Gradient Algorithm

This paper deals with the parameter identication problem for Hammerstein systems with two-segment preload nonlinearity. Taking into account the complexity of Hammerstein systems, we use theWeierstrass approximation theorem to convert a Hammerstein system into a special form that has linear-in-parameters, and propose a stochastic gradient algorithm to estimate all unknown parameters of Hammerstein systems. Furthermore, a modified stochastic gradient algorithm is given to improve the convergence rate. The applicability of the approach is illustrated by a simulation example.

Sign in / Sign up

Export Citation Format

Share Document