The Padé-Rayleigh-Ritz method for solving large Hermitian eigenproblems (Q1911447)

The method described uses Padé approximants and the Krylov sequence \(x, Ax, \dots, A^{m - 1} x\) to compute a few Ritz eigenvalues of a large sparse Hermitian matrix \(A\) of order \(n\). The method approximates the poles of \(((I - \lambda A)^{-1} x,x)\) by those of its Padé approximant of order \(m (\ll n)\). The relationship of the method to the Lanczos method is discussed, with special emphasis on stability and suitability for parallel computation.