scholarly journals Matrix Transformations and Quasi-Newton Methods

2007 ◽  
Vol 2007 ◽  
pp. 1-17
Author(s):  
Boubakeur Benahmed ◽  
Bruno de Malafosse ◽  
Adnan Yassine
Keyword(s):  
Linear System ◽  
Newton Method ◽  
Matrix Transformations ◽  
Newton Methods ◽  
Tridiagonal Matrices ◽  
Finite Section ◽  
Finite Section Method ◽  
Quasi Newton ◽  
Infinite Linear System ◽  
Infinite Linear

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the formssξ,sξ∘,sξ(c), orlp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear system.

Research on BP Neural Network Algorithm Based on Quasi-Newton Method

2014 ◽  
Vol 686 ◽  
pp. 388-394 ◽  
Author(s):  
Pei Xin Lu
Keyword(s):  
Neural Network ◽  
Empirical Analysis ◽  
Newton Method ◽  
Bp Neural Network ◽  
Bp Algorithm ◽  
Newton Methods ◽  
Network Algorithm ◽  
Neural Network Algorithm ◽  
Quasi Newton ◽  
Improved Bp Algorithm

With more and more researches about improving BP algorithm, there are more improvement methods. The paper researches two improvement algorithms based on quasi-Newton method, DFP algorithm and L-BFGS algorithm. After fully analyzing the features of quasi-Newton methods, the paper improves BP neural network algorithm. And the adjustment is made for the problems in the improvement process. The paper makes empirical analysis and proves the effectiveness of BP neural network algorithm based on quasi-Newton method. The improved algorithms are compared with the traditional BP algorithm, which indicates that the improved BP algorithm is better.

scholarly journals Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces

2020 ◽  
Vol 36 (36) ◽  
pp. 570-586 ◽  
Author(s):  
Fernando Pablos Romo ◽  
Víctor Cabezas Sánchez
Keyword(s):  
Linear System ◽  
Vector Spaces ◽  
Inner Product ◽  
Dimensional Vector ◽  
Product Spaces ◽  
Infinite Dimensional ◽  
Inner Product Spaces ◽  
Linear Maps ◽  
Infinite Linear System ◽  
Infinite Linear

The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in \text{Mat}_{n\times m} ({\mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, the least norm solution of an infinite linear system from the Moore-Penrose inverse offered is studied.

scholarly journals A new class of self-scaling for quasi-newton method based on the quadratic model

2021 ◽  
Vol 21 (3) ◽  
pp. 1830
Author(s):  
Basim A. Hassan ◽  
Ranen M. Sulaiman
Keyword(s):  
Newton Method ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Quadratic Model ◽  
Newton Methods ◽  
New Class ◽  
Unconstrained Optimization Problems ◽  
The Common ◽  
Numerical Performance ◽  
Quasi Newton

<span id="docs-internal-guid-a04d8b24-7fff-eaad-9449-fe4b2527904b"><span>Quasi-Newton method is an efficient method for solving unconstrained optimization problems. Self-scaling is one of the common approaches in the modification of the quasi-Newton method. A large variety of self-scaling of quasi-Newton methods is very well known. In this paper, based on quadratic function we derive the new self-scaling of quasi-Newton method and study the convergence property. Numerical results on the collection of problems showed the self-scaling of quasi-Newton methods which improves overall numerical performance for BFGS method.</span></span>

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

scholarly journals A Broyden Class of Quasi-Newton Methods for Riemannian Optimization

2015 ◽  
Vol 25 (3) ◽  
pp. 1660-1685 ◽  
Author(s):  
Wen Huang ◽  
K. A. Gallivan ◽  
P.-A. Absil
Keyword(s):  
Newton Methods ◽  
Riemannian Optimization ◽  
Broyden Class ◽  
Quasi Newton

Quasi-Newton methods for saddlepoints

1985 ◽  
Vol 47 (4) ◽  
pp. 393-399 ◽  
Author(s):  
F. Biegler-König
Keyword(s):  
Newton Methods ◽  
Quasi Newton
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