ISSN:
0945-3245
Keywords:
AMS(MOS): 65F 15
;
65-04
;
15-04
;
15A 33
;
81-04
;
CR: G 1.3
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary This paper extends the Francis QR algorithm to quaternion and antiquaternion matrices. It calculates a quaternion version of the Schur decomposition using quaternion unitary similarity transformations. Following a finite step reduction to a Hessenberg-like condensed form, a sequence of implicit QR steps reduces the matrix to triangular form. Eigenvalues may be read off the diagonal. Eigenvectors may be obtained from simple back substitutions. For serial computation, the algorithm uses only half the work and storage of the unstructured Francis QR iteration. By preserving quaternion structure, the algorithm calculates the eigenvalues of a nearby quaternion matrix despite rounding errors.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01395873
Permalink
