求解单调非线性方程和信号恢复问题的新三项共轭梯度算法

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED International Journal of Computer Mathematics Pub Date : 2023-07-23 DOI:10.1080/00207160.2023.2239947

A. Abubakar, P. Kumam, Jin-kui Liu, Hassan Mohammad, C. Tammer

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引用次数: 0

摘要

本文提出了一种新的求解非线性单调方程的三项投影算法。本文的目的是构造一个求非线性单调方程近似解的有效的竞争性算法。这是基于对满足下降充分条件的共轭梯度方向的一种新的选择。在Lipschitz连续性和所涉及算子单调性条件下，证明了算法的收敛性。数值实验表明，与现有算法相比，该算法所需的迭代次数较少。并将该算法应用于解决信号恢复问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems

This work presents a new three-term projection algorithm for solving nonlinear monotone equations. The paper is aimed at constructing an efficient and competitive algorithm for finding approximate solutions of nonlinear monotone equations. This is based on a new choice of the conjugate gradient direction which satisfies the sufficient descent condition. The convergence of the algorithm is shown under Lipschitz continuity and monotonicity of the involved operator. Numerical experiments presented in the paper show that the algorithm needs a less number of iterations in comparison with existing algorithms. Furthermore, the proposed algorithm is applied to solve signal recovery problems.

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

期刊介绍： International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.