QR Algorithm

The QR algorithm, or QR iteration, is an eigenvalue algorithm used to calculate the eigenvalues and eigenvectors of a matrix. It was developed in the late 1950s by John G. F. Francis and, independently, by Vera N. Kublanovskaya. The basic method performs a QR decomposition of the matrix into an orthogonal matrix and an upper triangular matrix, multiplies the two factors back together in reverse order, and repeats the process, with the matrix converging toward a form that reveals its eigenvalues.