Iterative Computation of Higher Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors
Alan L Andrew, Roger C. E. Tan · Birkhäuser Basel eBooks · 2002
This paper is concerned with iterative methods for computing partial derivatives of eigenvalues and eigenvectors of matrix-valued functions of several real variables. First, an analysis is given of a previously announced method which computes mixed partial derivatives of simple eigenvalues and the corresponding eigenvectors and also second order mixed partial derivatives of repeated eigenvalues. Next a new method for computing third order partial derivatives of repeated eigenvalues and second order derivatives of the corresponding eigenvectors is presented and its key properties are established. Efficiency and numerical stability are considered as well as theoretical convergence. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.