欠定非线性系统极小二范数解的可信误差界

Journal of Jilin University Science Edition

Previous Articles Next Articles

Verified Error Bounds for Minimum 2Norm Solutionsof Underdetermined Nonlinear Systems

LI Zhe^1,2,3, SANG Haifeng^4, XU Weihua¹

1. School of Science, University of Science and Technology, Changchun 130022, China;2. Automated Reasoning and Cognition Key Laboratory of Chongqing, Chongqing 400714, China; 3. Key Lab ofSymbolic Computation and Knowledge Engineering of Ministry of Education, Changchun 130012, China;4. College of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China

Received:2014-10-13 Online:2015-05-26 Published:2015-05-21
Contact: SANG Haifeng E-mail:sanghaifeng2008@163.com

Abstract

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.

Key words: underdetermined system, minimum 2norm solution, verification

CLC Number:

O241.3

LI Zhe, SANG Haifeng, XU Weihua. Verified Error Bounds for Minimum 2Norm Solutionsof Underdetermined Nonlinear Systems[J].Journal of Jilin University Science Edition, 2015, 53(03): 414-418.

[1]	JIANG Xue, CUI Kai. Discretization Problems of a Class of Multivariate Hermite-Type Interpolation [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1117-1123.
[2]	YANG Xiaoying. An Anisotropic Optimal Perfectly Matched LayerMethod for Solving Scattering Problems#br# [J]. Journal of Jilin University Science Edition, 2018, 56(5): 1073-1078.
[3]	YANG Xiaoying. Convergence of Optimal PML Method for 3D TimeHarmonic Electromagnetic Scattering Problems [J]. Journal of Jilin University Science Edition, 2018, 56(2): 293-298.
[4]	YANG Xiaoying, WANG Xiaoyang. Convergence of Optimal Perfectly Matched LayerMethod for Elastic Wave Scattering Problems [J]. Journal of Jilin University Science Edition, 2017, 55(06): 1425-1429.
[5]	YANG Xiaoying, DU Xinwei. Convergence of Uniaxial Optimal PML Methodfor TimeDomain Acoustic Scattering Problems [J]. Journal of Jilin University Science Edition, 2017, 55(03): 587-593.
[6]	YANG Xiaoying. Convergence of Single Axis Optimal Perfectly Matched LayerMethod for Scattering Problems in TwoLayered Media [J]. Journal of Jilin University Science Edition, 2016, 54(05): 983-988.
[7]	YANG Xiaoying. Convergence of Optimal Perfectly MatchedLayer Method for Scattering Problems [J]. Journal of Jilin University Science Edition, 2016, 54(04): 709-714.
[8]	KE Xianbin, LIU Hongwei, YOU Hailong. Efficient Global Optimization Algorithm Based on Gradient Method [J]. Journal of Jilin University Science Edition, 2016, 54(01): 40-44.
[9]	JING Ke, ZHU Gongqin. A Rational Interpolation Algorithm of Higher Order Derivative [J]. Journal of Jilin University Science Edition, 2015, 53(03): 389-394.
[10]	LI Zhe, SUN Yan. Error Formulas of Lagrange Projectors for Cartesian Point Sets [J]. Journal of Jilin University Science Edition, 2014, 52(05): 911-915.
[11]	LI Zhe, YIN Weishi, YANG Hua. Certification of the Square Structure Matrix with Rank Deficiency k [J]. Journal of Jilin University Science Edition, 2014, 52(03): 465-469.
[12]	ZHANG Lanhui, LI Yonghai. FifthOrder Finite Volume Method Based onthe Lobatto-Gauss Constructure [J]. Journal of Jilin University Science Edition, 2014, 52(03): 397-407.
[13]	LI Zhe, ZHOU Rui. Certification of Square Structure Matrix with Rank Deficiency One [J]. Journal of Jilin University Science Edition, 2013, 51(06): 1101-1103.
[14]	YANG Xiao-Yang, WANG Yi-Ni. An Optimal Perfectly Matched Layer Technique forUniaxial Scattering Problems [J]. J4, 2013, 51(01): 89-91.
[15]	ZHANG Ye, MA Yunyun. Numerical Method to Reconstruction of Grating [J]. J4, 2012, 50(4): 654-662.

Verified Error Bounds for Minimum 2Norm Solutionsof Underdetermined Nonlinear Systems

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0