Accelerating the convergence of an iterative method for derivatives of eigensystems (Q1087310)

The author studies an iterative method of Rudisill and Chu, as extended by the reviewer [J. Inst. Math. Appl. 24, 209-218 (1979; Zbl 0443.65020)], for computing partial derivatives of the dominant eigenvalue and the corresponding eigenvector of a matrix which depends smoothly on a number of parameters. His main result is that the performance of the method is dramatically improved by the use of the vector \(\epsilon\)- algorithm. Subsequently the author [IMA J. Numer. Anal. to appear] has extended this work to subdominant eigenvalues and given a more complete theoretical analysis of the problem and the author [Appl. Numer. Math., to appear] has obtained similar results for the topological \(\epsilon\)- algorithm. These results make the iterative approach for the first time truly competitive with the more popular direct methods for realistic problems.