求解非线性不适定问题的一种有效离散化方法

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2023-06-15 DOI:10.1515/cmam-2021-0146
M. Rajan, J. Jose
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引用次数: 1

摘要

摘要基于信息的复杂性分析在求解各种实际问题的计算中具有重要的意义。计算解所需的离散信息量在问题的计算复杂度中起着重要的作用。虽然这种方法已经成功地应用于线性问题,但在文献中还没有努力将其应用于非线性问题。本文通过考虑一种有效的离散化方法来离散非线性不适定问题来解决这一问题。我们在一个简化的高斯-牛顿迭代方法的背景下应用离散化方案,并表明我们的方案只需要少量的信息来计算解。给出了收敛性分析和误差估计。数值算例说明了该方案的可行性。理论和数值研究表明,该格式可用于求解非线性问题。
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An Efficient Discretization Scheme for Solving Nonlinear Ill-Posed Problems
Abstract Information based complexity analysis in computing the solution of various practical problems is of great importance in recent years. The amount of discrete information required to compute the solution plays an important role in the computational complexity of the problem. Although this approach has been applied successfully for linear problems, no effort has been made in literature to apply it to nonlinear problems. This article addresses this problem by considering an efficient discretization scheme to discretize nonlinear ill-posed problems. We apply the discretization scheme in the context of a simplified Gauss–Newton iterative method and show that our scheme requires only less amount of information for computing the solution. The convergence analysis and error estimates are derived. Numerical examples are provided to illustrate the fact that the scheme can be implemented successfully. The theoretical and numerical study asserts that the scheme can be employed to nonlinear problems.
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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