Convergence of theQR algorithm

TheQR algorithm ofJ. G. F. Francis is used in computing matrix eigenvalues. The convergence proof given here is an analogue ofRutishauser's proof of the convergence of theLR algorithm, but our proof covers the case of disorder of the eigenvalues.The work presented in this paper was supported by the AEC Computing and Applied Mathematics Center, Courant Institute of Mathematical Sciences, New York University, under contract AT(30-1)-1480 with the U.S.Atomic Energy Commission.