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欠定非线性系统极小二范数解的可信误差界
Verified Error Bounds for Minimum 2-Norm Solutions of Underdetermined Nonlinear Systems
【摘要】 考虑欠定非线性系统极小二范数解的可信验证问题.欠定非线性系统的极小二范数解为解向量二范数的极小值点,对给定的欠定非线性系统,将方形非线性系统单根的可信验证方法与对称正定矩阵的可信验证方法相结合,给出计算Jacobi矩阵为列满秩欠定非线性系统极小二范数解的可信误差界算法.
【Abstract】 This paper deals with the verification for minimum 2-norm solutions of underdetermined nonlinear systems.The minimum 2-norm solution of underdetermined nonlinear system is the minimum point of the 2-norm of solution vectors.For the given undetermined nonlinear system,combining the verification for simple solutions of square systems with the verification for symmetric positive definite matrices presented an algorithm for verifying minimum 2-norm solutions of underdetermined nonlinear systems with full rank Jacobian matrices.
【关键词】 欠定系统；
极小二范数解；
可信验证；
【Key words】 underdetermined system； minimum 2-norm solution； verification；
【Key words】 underdetermined system； minimum 2-norm solution； verification；
【基金】 国家自然科学基金(批准号:11326209;11171133;91118001);自动推理与认知重庆市重点实验室开放课题基金(批准号:CARC2014002)
- 【文献出处】 吉林大学学报(理学版) ,Journal of Jilin University(Science Edition) , 编辑部邮箱 ,2015年03期
- 【分类号】O241.7
- 【被引频次】1
- 【下载频次】88