Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 37-45.

• Articles • Previous Articles     Next Articles

Structured Matrix Nearness Problem with Least Square Spectra Constraint and Its Perturbation Analysis

 XIE Dong-Xiu1,2, ZHANG Zhong-Zhi3   

  1. 1.School of Science, Beijing Information Science and Technology University, Beijing 100192;
    2.College of Mathematics and Econometrics, Hunan University, Changsha 410082;
    3.Department of Mathematics, Dongguan University of Technology, Guangdong Dongguan 523808
  • Received:2011-11-09 Revised:2012-11-13 Online:2013-02-25 Published:2013-02-25
  • Supported by:

    北京市自然科学基金(1122015)和北京市属高等学校人才强教深化计划项目(PHR201006116)资助资助

Abstract:

A nearness matrix problem is considered with two constraints—least square spectra constraint, symmetric and skew-Hamiltonian structure. It discusses two problems: (I) the set L of symmetric and skew-Hamiltonian real n × n matrices A to minimize the Frobenius norm of AX − X∧, where X, ∧ are eigenvector and eigenvalue matrices, respectively, and (II) find Â ∈ L such that C − Â = min AL ||CA||, where || ·|| is the Frobenius norm. A general form of elements in L is given and an explicit expression of the minimizer Â is derived. Perturbation theory of the nearest matrix is analyzed. A numerical example is reported.

Key words: Best approximation, Least squares problem, Perturbation theory

CLC Number: 

  • 41A50
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