Name
Title | ||
|---|---|---|
Analyticity of Semisimple Eigenvalues and Corresponding Eigenvectors of Matrix-Valued Functions. |
Abstract | ||
|---|---|---|
In this paper, we study the analyticity of the semisimple eigenvalue and the corresponding eigenvector functions of general analytic matrix-valued functions which are very important in many engineering applications such as the optimum design of dynamical structures, model updating, damage detecting, quantum mechanics, diffraction grating theory, medical imaging, and social network theory. We establish some new sufficient conditions on existence of analytic eigenvalue and eigenvector functions corresponding to semisimple eigenvalues of general analytic matrix-valued functions, which relaxes the condition in [P. Lancaster, A. S. Markus, and F. Zhou, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 606-626]. We also present a numerical method to compute the derivatives of the eigenvalue and eigenvector functions. Numerical performance of the method is illustrated by some numerical examples. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/151003799 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
analytic eigenvalue and eigenvector functions,semisimple eigenvalues,matrix-valued functions | Mathematical analysis,Matrix (mathematics),Generalized eigenvector,Numerical analysis,Eigenvalues and eigenvectors,Mathematics,Inverse iteration | Journal |
Volume | Issue | ISSN |
36 | 4 | 0895-4798 |
Citations | PageRank | References |
2 | 0.40 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jiang Qian | 1 | 7 | 2.66 |
| Delin Chu | 2 | 24 | 2.72 |
| Roger C. E. Tan | 3 | 102 | 19.13 |