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SEMI-DEFINITE PROGRAMMING TECHNIQUES FOR STRUCTURED QUADRATIC INVERSE EIGENVALUE PROBLEMS.

Matthew M Lin1, Bo Dong2, Moody T Chu3

  • 1Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205. ( mlin@ncsu.edu ). This research was supported in part by the National Science Foundation under grants DMS-0505880 and DMS-0732299.

Numerical Algorithms
|November 14, 2014
PubMed
Summary
This summary is machine-generated.

Semi-definite programming (SDP) offers a powerful approach to solving complex quadratic inverse eigenvalue problems (QIEPs). This method simplifies the formulation and effectively addresses challenges in vibration system engineering.

Keywords:
inverse eigenvalue problemmodel updatingquadratic pencilsemi-definite programmingstructural constraint

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Area of Science:

  • Engineering
  • Mathematics
  • Computational Science

Background:

  • Quadratic inverse eigenvalue problems (QIEPs) are crucial for modeling and updating dynamic systems in engineering.
  • QIEPs present significant theoretical and computational challenges due to diverse structural constraints.

Purpose of the Study:

  • To introduce an innovative application of semi-definite programming (SDP) techniques for solving QIEPs.
  • To demonstrate the effectiveness of SDP in addressing complex QIEP challenges.

Main Methods:

  • Application of semi-definite programming (SDP) to quadratic inverse eigenvalue problems (QIEPs).
  • Development of a uniform and simple SDP formulation for QIEPs.

Main Results:

  • SDP provides a powerful and versatile tool for a wide range of problems.
  • The proposed SDP formulation effectively solves many difficult QIEPs.

Conclusions:

  • SDP offers a unified and simplified approach to tackling QIEPs.
  • This method enhances the feasibility of constructing and updating vibration systems in engineering applications.