QR algorithm

In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was developed in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya, working independently.[1][2][3] The basic idea is to perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the reverse order, and iterate.

  1. ^ J.G.F. Francis, "The QR Transformation, I", The Computer Journal, 4(3), pages 265–271 (1961, received October 1959). doi:10.1093/comjnl/4.3.265
  2. ^ Francis, J. G. F. (1962). "The QR Transformation, II". The Computer Journal. 4 (4): 332–345. doi:10.1093/comjnl/4.4.332.
  3. ^ Vera N. Kublanovskaya, "On some algorithms for the solution of the complete eigenvalue problem," USSR Computational Mathematics and Mathematical Physics, vol. 1, no. 3, pages 637–657 (1963, received Feb 1961). Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, vol.1, no. 4, pages 555–570 (1961). doi:10.1016/0041-5553(63)90168-X