A projection method for the computation of inner eigenvalues using high degree rational operators (Q2471832)

This paper concerns matrices \(A\) that have a real spectrum and an orthonormal eigenbasis. The problem is the computation of the inner eigenvalues of \(A\) in a given interval \((a, b)\) such that neither \(a\) nor \(b\) is an eigenvalue of \(A\). The method is a projection technique that does not presuppose the spectrum of \(A\) to be known. The computation requires only a few multiplications of matrices and an inversion such that for some classes of matrices the algorithm is almost of linear complexity. Rounding errors are substantially reduced by a preprocessing that modifies the eigenvalues, leaving those in \((a, b)\) almost unchanged.