# Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form

@inproceedings{Adlerborn2000ParallelTR, title={Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form}, author={Bj{\"o}rn Adlerborn and Krister Dackland and Bo K{\aa}gstr{\"o}m}, booktitle={PARA}, year={2000} }

A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-triangular form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-triangular form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper triangular. In stage two, the desired upper Hessenberg-triangular form is computed using two-sided Givens rotations. Performance results for the ScaLAPACK-style implementations show that the parallel algorithms can…

## 13 Citations

### Parallel Reduction of a Block Hessenberg-Triangular Matrix Pair to Hessenberg-Triangular Form — Algorithm Design and Performance Results

- Computer Science
- 2004

Performance results for the ScaLAPACK-style implementation show that the parallel algorithm can be used to solve large scale problems effectively.

### Parallel and Blocked Algorithms for Reduction of a Regular Matrix Pair to Hessenberg-Triangular and Generalized Schur Forms

- Computer SciencePARA
- 2002

Algorithm and implementation issues regarding the single-/double-shift QZ algorithm are discussed and multishift strategies to enhance the performance in blocked as well as in parallell variants of the QZ method are described.

### A parallel Schur method for solving continuous-time algebraic Riccati equations

- Computer Science2008 IEEE International Conference on Computer-Aided Control Systems
- 2008

It is shown that the Schur method, based on computing the stable invariant subspace of a Hamiltonian matrix, can be parallelized in an efficient and scalable way.

### Parallel Solvers for Sylvester-Type Matrix Equations with Applications in Condition Estimation, Part I

- Computer ScienceACM Trans. Math. Softw.
- 2010

Parallel ScaLAPACK-style algorithms for solving eight common standard and generalized Sylvester-type matrix equations and various sign and transposed variants are presented. All algorithms are…

### RECSY and SCASY Library Software: Recursive Blocked and Parallel Algorithms for Sylvester-Type Matrix Equations with Some Applications

- Computer Science, Mathematics
- 2009

In this contribution, we review state-of-the-art high-performance computing software for solving common standard and generalized continuous-time and discrete-time Sylvester-type matrix equations. The…

### Contributions to Parallel Algorithms for Sylvester-type Matrix Equations and Periodic Eigenvalue Reordering in Cyclic Matrix Products

- Mathematics, Computer Science
- 2005

A direct method for periodic eigen value reordering in the periodic real Schur form which extends earlier work on the standard and the generalized eigenvalue problems.

### Efficient Reduction from Block Hessenberg Form to Hessenberg Form Using Shared Memory

- Computer SciencePARA
- 2010

A new cache-efficient algorithm for reduction from block Hessenberg form to Hessenburg form with one level of look-ahead in combination with a dynamic load-balancing scheme reduces the idle time and allows the use of coarse-grained tasks.

### Distributed One-Stage Hessenberg-Triangular Reduction with Wavefront Scheduling

- Computer ScienceSIAM J. Sci. Comput.
- 2018

A novel parallel formulation of Hessenberg-triangular reduction of a regular matrix pair on distributed memory computers is presented, based on a sequential cache-blocked algorit ...

### I/O Efficient Algorithms for Matrix Computations

- Computer ScienceArXiv
- 2010

It is shown that techniques like rescheduling of computational steps, appropriate choosing of the blocking parameters and incorporating of more matrix-matrix operations, can be used to improve the I/O and seek complexities of matrix computations.

### Algorithms and Library Software for Periodic and Parallel Eigenvalue Reordering and Sylvester-Type Matrix Equations with Condition Estimation

- Computer Science
- 2007

This Thesis contains contributions in two different but closely related subfields of Scientific and Parallel Computing which arise in the context of various eigenvalue problems: periodic and parall…

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