On a block implementation of Hessenberg multishift QR iteration
International Journal of High Speed Computing
Fundamentals of matrix computations
Fundamentals of matrix computations
Shifting strategies for the parallel QR algorithm
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
ScaLAPACK user's guide
LAPACK Working Note 68: A Parallel Algorithm for the Reduction of a Nonsymmetric Matrix to Block Upper-Hessenberg Form
LAPACK Working Note 72: The Computation of Elementary Unitary Matrices
LAPACK Working Note 72: The Computation of Elementary Unitary Matrices
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
Parallel Implementation of the Nonsymmetric QR Algorithm forDistributed Memory Architectures
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A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be directly computed using a parallel QR algorithm.This parallel complex Schur decomposition routine was developed to fill a void in the ScaLAPACK library and was based on the parallel real Schur decomposition routine already in ScaLAPACK. The real-arithmetic version was appropriately modified to make it work with complex arithmetic and implement a complex multiple bulge QR algorithm. This also required the development of new auxiliary routines that perform essential operations for the complex Schur decomposition, and that will provide additional linear algebra computation capability to the parallel numerical library community.