Some acceleration methods for iterative computer of derivatives of eigenvalues and eigenvectors

The performance of an iterative method for computing partial derivatives of eigenvalues and eigenvectors of parameter dependent matrices may be improved dramatically by various extrapolation methods proposed here. With exact computation, all these extrapolation methods yield the exact solution with a finite number of iterations. Two of these methods, which have not been used before for this problem, are compared with the ϵ‐algorithms. Numerical examples are given. The methods suggested may be used to obtain either highly accurate estimates or cheap estimates of modest accuracy.