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The QZ algorithm reduces a regular matrix pair to generalized Schur form, which can be used to address the generalized eigenvalue problem. This paper summarizes recent work on improving the performance of the QZ algorithm on serial machines and work in progress on a novel parallel implementation. In both cases, the QZ iterations are based on chasing chains… (More)

A parallel two-stage ScaLAPACK-style algorithm for reduction of a regular matrix pair (A; B) to Hessenberg-triangular form is presented. Stage one reduces the matrix pair to (Hr; T) form where Hr is upper r-Hessenberg with r subdiagonals and T is upper triangular. In the second stage of the reduction algorithm all but one of the subdi-agonals of the upper… (More)

Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm by Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importance, little attention has been paid to the parallelization of the QZ algorithm. The purpose of this work… (More)

A novel parallel formulation of Hessenberg-triangular reduction of a regular matrix pair on distributed memory computers is presented. The formulation is based on a sequential cache-blocked algorithmOrtí (2008). A static scheduling algorithm is proposed that addresses the problem of underutilized processes caused by two-sided updates of matrix pairs based… (More)

- Björn Adlerborn
- 2016

We present and discuss algorithms and library software for solving the generalized non-symmetric eigenvalue problem (GNEP) on high performance computing (HPC) platforms with distributed memory. Such problems occur frequently in computational science and engineering, and our contributions make it possible to solve GNEPs fast and accurate in parallel using… (More)

- Björn Adlerborn, Bo Kågström, Daniel Kressner, PDHGEQZ User Guide, Bo K̊agström
- 2016

Given a general matrix pair (A, B) with real entries, we provide software routines for computing a generalized Schur decomposition (S, T). The real and complex conjugate pairs of eigenvalues appears as 1×1 and 2×2 blocks, respectively, along the diagonals of (S, T) and can be reordered in any order. Typically, this functionality is used to compute… (More)

Recent improvements to the QZ algorithm for solving generalized eigenvalue problems are summarized. Among the major modifications are novel multishift QZ iterations based on chasing chains of tiny bulges and an extension of the so called aggressive early deflation strategy. The former modification aims to improve the execution time of the QZ algorithm on… (More)

- Björn Adlerborn
- 2004

The design, implementation and performance of a parallel algorithm for reduction of a matrix pair in block upper Hessenberg-Triangular form (H r , T) to upper Hessenberg-triangular form (H, T) is presented. This reduction is the second stage in a two-stage reduction of a regular matrix pair (A, B) to upper Hessenberg-Triangular from. The desired upper… (More)

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