scholarly journals On solving efficient matrix-free method via quasi-Newton approach for solving system of nonlinear equations

2021 ◽  
Vol 5 (4) ◽  
pp. 568-579
Author(s):  
Nopparat WAİROJJANA ◽  
Muhammad ABDULLAHI ◽  
Abubakar HALİLU ◽  
Aliyu AWWAL ◽  
Nuttapol PAKKARANANG
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Quasi Newton ◽  
Matrix Free

scholarly journals A Projection Hestenes–Stiefel Method with Spectral Parameter for Nonlinear Monotone Equations and Signal Processing

2020 ◽  
Vol 25 (2) ◽  
pp. 27
Author(s):  
Aliyu Muhammed Awwal ◽  
Lin Wang ◽  
Poom Kumam ◽  
Hassan Mohammad ◽  
Wiboonsak Watthayu
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Gradient Methods ◽  
System Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Sufficient Descent Condition ◽  
Monotone Equations ◽  
Matrix Free ◽  
Lipschitzian Continuous

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve ℓ 1 -norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising.

scholarly journals Efficient matrix-free direction method with line search for solving large-scale system of nonlinear equations

2020 ◽  
Vol 30 (4) ◽  
pp. 399-412
Author(s):  
Abubakar Halilu ◽  
Mohammed Waziri ◽  
Ibrahim Yusuf
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Line Search ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Inexact Line Search ◽  
Large Scale Problems ◽  
Scale Test ◽  
Line Search Technique ◽  
Matrix Free

We proposed a matrix-free direction with an inexact line search technique to solve system of nonlinear equations by using double direction approach. In this article, we approximated the Jacobian matrix by appropriately constructed matrix-free method via acceleration parameter. The global convergence of our method is established under mild conditions. Numerical comparisons reported in this paper are based on a set of large-scale test problems and show that the proposed method is efficient for large-scale problems.

scholarly journals An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
M. Y. Waziri ◽  
Z. A. Majid
Keyword(s):  
Nonlinear Equations ◽  
Line Search ◽  
Step Length ◽  
Search Strategies ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Convergence Results ◽  
Overall Performance ◽  
Predictor Corrector ◽  
Matrix Free

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.

Modified matrix-free methods for solving system of nonlinear equations

Optimization ◽  
2020 ◽  
pp. 1-20
Author(s):  
Mohammed Yusuf Waziri ◽  
Hadiza Usman Muhammad ◽  
Abubakar Sani Halilu ◽  
Kabiru Ahmed
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Matrix Free

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

Finding and Verifying All Solutions of a System of Nonlinear Equations

1998 ◽  
Vol 31 (16) ◽  
pp. 327-332
Author(s):  
Max E. Jerrell
Keyword(s):  
Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
All Solutions

scholarly journals Typical curve with G1 constraints for curve completion

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Chuan He ◽  
Gang Zhao ◽  
Aizeng Wang ◽  
Fei Hou ◽  
Zhanchuan Cai ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Interpolation Problem ◽  
Sufficient Conditions ◽  
System Of Nonlinear Equations ◽  
Simple Construction ◽  
Completion Task ◽  
Curve Completion ◽  
Novel Algorithm

AbstractThis paper presents a novel algorithm for planar G1 interpolation using typical curves with monotonic curvature. The G1 interpolation problem is converted into a system of nonlinear equations and sufficient conditions are provided to check whether there is a solution. The proposed algorithm was applied to a curve completion task. The main advantages of the proposed method are its simple construction, compatibility with NURBS, and monotonic curvature.

Quantum Newton’s Method for Solving the System of Nonlinear Equations

SPIN ◽  
2021 ◽  
pp. 2140004
Author(s):  
Cheng Xue ◽  
Yuchun Wu ◽  
Guoping Guo
Keyword(s):  
Quantum Computing ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Data Conversion ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
System Of Linear Equations ◽  
Whole Process

While quantum computing provides an exponential advantage in solving the system of linear equations, there is little work to solve the system of nonlinear equations with quantum computing. We propose quantum Newton’s method (QNM) for solving [Formula: see text]-dimensional system of nonlinear equations based on Newton’s method. In QNM, we solve the system of linear equations in each iteration of Newton’s method with quantum linear system solver. We use a specific quantum data structure and [Formula: see text] tomography with sample error [Formula: see text] to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is [Formula: see text]. Through numerical simulation, we find that when [Formula: see text], QNM is still effective, so the complexity of QNM is sublinear with [Formula: see text], which provides quantum advantage compared with the optimal classical algorithm.

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