ABSTRACT
QR method of computing eigenvalues An iterative method of finding all of the eigenvalues of an n × n matrix A. Let A0 = A. Determine A1, A2, . . . , Am, . . . in the following way: If A is a real tridiagonal matrix or a complex upper Hessenberg matrix, let sm be the eigenvalue of the 2×2 matrix closer to a(m)nn in the lower right corner of Am, or if A is a real upper Hessenberg matrix, let sm and sm+1 be the eigenvalues of the 2×2 matrix in the lower right corner of Am. With this (these) value(s) of sm, write Am − smI as QmRm, where Qm is a unitary matrix and Rm is an upper Hessenberg matrix. Then define Am+1 = RmQm − smI . Then the elements on the diagonal of limm→∞ Am converge to the eigenvalues of A.
