An affine inverse eigenvalue problem

Affine inverse eigenvalue problems are usually solved using iterations where the object is to diminish the difference between a set of prescribed eigenvalues and those calculated during iteration. Such an approach requires a scheme for pairing the eigenvalues consistently throughout the iterative process. There appears to be no obvious criterion for such pairing for problems with complex eigenvalues. Consequently the methods previously proposed in the literature are restricted to symmetric eigenvalue problems with real eigenvalues. Real eigenvalues can be paired using their natural increasing order. This paper presents a new Newton's iteration based method where the subject of iteration is the affine coefficients set. With the new method proposed the non-symmetric inverse eigenvalue problem, with inherent complex eigenvalues can be solved, as well as problems associated with symmetric pencils of high order. An immediate application presented in the paper deals with the reconstruction and passive control of damped vibratory systems.