EXACT NTH DERIVATIVES OF EIGENVALUES AND EIGENVECTORS

Computing derivatives of eigenvalues and eigenvectors is of considerable importance in mathematics, physics, and engineering. These derivatives are essential for sensitivity analysis, which is used to study the effect of change in various parameters of an eigensystem on its performance. General solutions of eigenfunctions' derivatives have not been available. In this paper, exact analytical solutions for the nth derivatives of unrepeated eigenvalues and corresponding eigenvectors are given for general nonlinear and linear eigenvalue problems. The application of the theory is illustrated with examples.