A note on computing eigenvector derivatives with distinct and repeated eigenvalues. (English) Zbl 1111.65034
Summary: A new method for computing eigenvector derivatives with distinct and repeated eigenvalues for the real symmetric eigensystems is presented. Its main idea is to extend the governing equations of particular solutions for eigenvector derivatives. The extension is completed by requiring the solution to be mass orthogonal with respect to the distinct or repeated modes and adjusting the corresponding coefficients so that the coefficient matrix of the extended system is nonsingular and has smaller condition number. Numerical examples are included to demonstrate the validity of the proposed method.
MSC:
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
Keywords:
symmetric eigensystems; distinct and repeated eigenvalues; eigenvector derivatives; extended system; condition numbers; numerical examplesReferences:
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