Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Numerical algorithm
|
| gptkbp:appliesTo |
Complex matrices
Real matrices |
| gptkbp:category |
Eigenvalue algorithms
Matrix algorithms |
| gptkbp:citation |
Kublanovskaya, V. N. (1961). On some algorithms for the solution of the complete eigenvalue problem.
Francis, J. G. F. (1961). The QR Transformation, Part I & II. |
| gptkbp:complexity |
O(n^3) per iteration
|
| gptkbp:convergesTo |
Schur form
|
| gptkbp:field |
gptkb:Numerical_linear_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
The QR Algorithm
|
| gptkbp:implementedIn |
gptkb:MATLAB
gptkb:NumPy gptkb:LAPACK |
| gptkbp:improves |
Hessenberg form reduction
Implicitly shifted QR algorithm |
| gptkbp:input |
Square matrix
|
| gptkbp:introduced |
gptkb:John_G.F._Francis
gptkb:Vera_N._Kublanovskaya |
| gptkbp:introducedIn |
1961
|
| gptkbp:output |
Eigenvalues
Eigenvectors |
| gptkbp:relatedTo |
gptkb:Schur_decomposition
QR decomposition Power iteration |
| gptkbp:step |
QR decomposition
Matrix multiplication |
| gptkbp:usedFor |
Computing eigenvalues
Computing eigenvectors |
| gptkbp:bfsParent |
gptkb:Top_Ten_Algorithms_of_the_20th_Century_(SIAM)
|
| gptkbp:bfsLayer |
8
|