QZ algorithm to solve the generalized eigenvalue problem for complex matrices. [In FORTRAN for IBM 370/195]

Journal Article · Fri Dec 01 04:00:00 EST 1978 · ACM Trans. Math. Software; (United States)

DOI:https://doi.org/10.1145/356502.356500· OSTI ID:5564606

Garbow, B S

Three FORTRAN subroutines are provided that implement a complex form of the QZ algorithm for finding lambda and z such that Az = lambda Bz, where A and B are complex N by N matrices. The complex QZ algorithm is unaffected by singularity or near singularity of B. Subroutie CQZHES implements the first step of the algorithm wherein A and B are simultaneously reduced by unitary transformations to upper Hessenberg and upper triangular form, respectively. Subroutine CQZVAL implements an iterative process that reduces A to upper triangular form while maintaining the trianglar form of B. The eigenvalues are derivable from the corresponding diagonal elements of the reduced A and B. Subroutine CQZVEC applies the accumulated transformations from the two earlier steps onto the eigenvectors of the triangular problem. No facility is provided for obtaining just a few eigenvectors or, for balancing A and B. A long-precision IBM version of the subroutines was tested on a 370/195. There are no machine-dependent constants in the subroutines, so the standard version should run directly on different machines. (RWR)

• Research Organization: Argonne National Lab., IL
• OSTI ID: 5564606
• Journal Information: ACM Trans. Math. Software; (United States), Journal Name: ACM Trans. Math. Software; (United States) Vol. 4:4; ISSN ACMSC
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
C CODES
CALCULATION METHODS
COMPUTER CODES
COMPUTERS
EIGENVALUES
FORTRAN
IBM COMPUTERS
MATHEMATICAL LOGIC
MATRICES
PROGRAMMING LANGUAGES