QR Decomposition Algorithm
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A QR Decomposition Algorithm is an eigenvalue algorithm based on QR transformations that can be applied by a QR system (to solve a QR decomposition task.
- Example(s):
- Counter-Example(s):
- See: Triangular Matrix, Eigenvalue Algorithm, Eigenvalue, Eigenvectors, QR Decomposition, Orthogonal Matrix.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/QR_algorithm Retrieved:2015-3-3.
- In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR transformation was developed in the late 1950s by John G.F. Francis (England) and by Vera N. Kublanovskaya (USSR), working independently. [1] 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.
- ↑ J.G.F. Francis, "The QR Transformation, I", The Computer Journal, vol. 4, no. 3, pages 265-271 (1961, received Oct 1959) online at oxfordjournals.org;
J.G.F. Francis, "The QR Transformation, II" The Computer Journal, vol. 4, no. 4, pages 332-345 (1962) online at oxfordjournals.org.
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).