基于奇异值分解的非线性系统流形解的数值计算
Numerical Computation of Manifold Solutions for Nonlinear Systems Based on Singular Value Decomposition
DOI: 10.12677/aam.2025.144134, PDF,   
作者: 高炜晰, 李育达, 丁嘉宇, 邓舒雨, 陈亭亭, 戈鹏鹤*：长春理工大学数学与统计学院，吉林 长春
关键词: 边界矩阵；正则解；数值计算；Boundary Matrix； Regular Solution； Numerical Computation
摘要: 本文利用边界矩阵技术，将非线性系统流形解的数值计算转化为增广非线性系统正则解的数值计算。利用雅可比矩阵的近似左零空间和右零空间构造增广矩阵，进而利用增广矩阵构造一族增广非线性系统，该族增广非线性系统中每个非线性系统均为给定非线性系统添加约束条件后的摄动系统，利用牛顿迭代更新增广非线性系统的解使得其逼近原非线性系统的流形解。
Abstract: In this paper, the numerical computation of manifold solutions of nonlinear systems is transformed into the numerical computation of regular solutions of augmented nonlinear systems using the boundary matrix technique. The approximate left-zero space and right-zero space of Jacobi matrix are used to construct the generalized matrix, and then the generalized matrix is used to construct a family of generalized nonlinear systems, and each nonlinear system in the family of generalized nonlinear systems is a regenerative system after the constraints are added to the given nonlinear system, and Newton iteration is utilized to update the solution of the generalized nonlinear system to make it approximate to the manifold solution of the original nonlinear system.
文章引用：高炜晰, 李育达, 丁嘉宇, 邓舒雨, 陈亭亭, 戈鹏鹤. 基于奇异值分解的非线性系统流形解的数值计算[J]. 应用数学进展, 2025, 14(4): 1-10. https://doi.org/10.12677/aam.2025.144134

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