求解积分方程的多尺度快速配置法
Multiscale Collocation Methods for Integral Equations
DOI: 10.12677/AAM.2017.64054, PDF, HTML, XML, 下载: 1,563  浏览: 2,499  国家自然科学基金支持
作者: 罗兴钧, 李丽君, 张荣：赣南师范大学数学与计算机科学学院，江西 赣州
关键词: 交替迭代法；扇形算子；多尺度配置法；Alternating Iterative Methods； A Sectorial Operator； Multiscale Collocation Methods
摘要: Banach空间中研究求解第一类Fredholm积分方程的多尺度配置方法。在积分算子是扇形紧算子时，采用Blance原理，给出迭代停止的选择方法，确保了近似解的最优收敛率。最后，给出算例说明了算法的有效性。
Abstract: Multiscale collocation methods are developed for solving ill-posed Fredholm integral equations of the first kind in Banach spaces. The optimal convergence rate of solution is given when the method is terminated by the balancing discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the proposed algorithm.
文章引用：罗兴钧, 李丽君, 张荣. 求解积分方程的多尺度快速配置法[J]. 应用数学进展, 2017, 6(4): 456-467. https://doi.org/10.12677/AAM.2017.64054

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