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...

R. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm...

and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the divide-and-conquer approach from...

or 28 pounds avoirdupois QR decomposition, a decomposition of a matrix QR algorithm, an eigenvalue algorithm to perform QR decomposition Quadratic reciprocity...

An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine...

A QR code (quick-response code) is a type of two-dimensional matrix barcode, invented in 1994, by Japanese company Denso Wave for labelling automobile...

most widely used algorithm for computing eigenvalues is John G. F. Francis' QR algorithm, considered one of the top ten algorithms of 20th century. Any...

Schur decomposition of a given matrix is numerically computed by the QR algorithm or its variants. In other words, the roots of the characteristic polynomial...

fast-multipole) Eigenvalue algorithms Arnoldi iteration Inverse iteration Jacobi method Lanczos iteration Power iteration QR algorithm Rayleigh quotient iteration...

transformation. The QR factorization is often used to solve linear least-squares problems, and eigenvalue problems (by way of the iterative QR algorithm). An LU factorization...

connection with the shifted QR algorithm for computing matrix eigenvalues. See Dekker and Traub The shifted QR algorithm for Hermitian matrices. Again...

Fortune's algorithm is a sweep line algorithm for generating a Voronoi diagram from a set of points in a plane using O(n log n) time and O(n) space. It...

product of the Q matrices from the steps in the algorithm. (For more general matrices, the QR algorithm yields the Schur decomposition first, from which...

O(m\log m)} operations. Some general eigendecomposition algorithms, notably the QR algorithm, are known to converge faster for tridiagonal matrices than...

which is solved by the QR algorithm. This algorithm was popular, but significantly more efficient algorithms exist. Algorithms based on the Newton–Raphson...

below the main diagonal of a matrix, to perform QR decompositions and in the first step of the QR algorithm. They are also widely used for transforming to...

diagonal matrix. If the matrix is not square the QR decomposition is performed first and then the algorithm is applied to the R {\displaystyle R} matrix....

published the QR algorithm for computing the eigenvalues and eigenvectors of matrices, which has been named as one of the ten most important algorithms of the...

The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity...

 6–8. Retrieved 2024-04-21. "NSA Releases Future Quantum-Resistant (QR) Algorithm Requirements for National Security Systems". National Security Agency...

efficiently, for instance with the QR algorithm, or somewhat related, Francis' algorithm. Also Francis' algorithm itself can be considered to be related...

plane of the two equal points). QR algorithm In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is, a procedure to calculate...

finding all the roots, arguably the most reliable method is the Francis QR algorithm computing the eigenvalues of the companion matrix corresponding to the...

known until the QR algorithm was designed in 1961. Combining the Householder transformation with the LU decomposition results in an algorithm with better...

simultaneously. 4. Set X = U Y V T . {\displaystyle X=UYV^{T}.} Using the QR algorithm, the real Schur decompositions in step 1 require approximately 10 ( m...

{\begin{pmatrix}1&0&0&0\\2&4&0&0\\0&3&3&0\\0&0&4&3\\\end{pmatrix}}.} One variant of the QR algorithm starts with reducing a general matrix into a bidiagonal one, and the...

eigenvalue problem. The most popular algorithm for this task is the QZ algorithm, which is an implicit version of the QR algorithm to solve the associated eigenvalue...

as shifted QR-factorization. In eigenvalue algorithms, the Hessenberg matrix can be further reduced to a triangular matrix through Shifted QR-factorization...

Odd round QR( 0, 4, 8, 12) // column 1 QR( 5, 9, 13, 1) // column 2 QR(10, 14, 2, 6) // column 3 QR(15, 3, 7, 11) // column 4 // Even round QR( 0, 1, 2...

proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth...