# Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking

@inproceedings{Jonsson2000ParallelTS, title={Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking}, author={Isak Jonsson and Bo K{\aa}gstr{\"o}m}, booktitle={PARA}, year={2000} }

We present recursive blocked algorithms for solving triangular Sylvester-type matrix equations. Recursion leads to automatic blocking that is variable and "squarish". The main part of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We also present new highly optimized superscalar kernels for solving small-sized matrix equations stored in level 1 cache. Hereby, a larger part of the total execution time will be spent in GEMM operations. In turn, this…

## 5 Citations

### Recursive blocked algorithms for solving triangular systems—Part I: one-sided and coupled Sylvester-type matrix equations

- Computer Science, MathematicsTOMS
- 2002

Novel recursive blocked algorithms for solving one-sided triangular matrix equations, including the continuous-time Sylvester and Lyapunov equations, and a generalized coupled SylvesTER equation are presented.

### Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software

- Computer ScienceSIAM Rev.
- 2004

Some of the recent advances made by applying the paradigm of recursion to dense matrix computations on today's memory-tiered computer systems are reviewed and details.

### A Faster and Simpler Recursive Algorithm for the LAPACK Routine DGELS

- Computer Science
- 2001

The four different problems of DGELS are essentially reduced to two, by use of explicit transposition of A, and by avoiding redundant computations in the update of B the authors reduce the work needed to compute the minimum norm solution.

### A NEW MUCH FASTER AND SIMPLERALGORITHM FOR LAPACK

- Computer Science
- 2000

The four diierent problems of DGELS are essentially reduced to two, by use of explicit transposition of A, and by avoiding redundant computations in the update of B the authors reduce the work needed to compute the minimum norm solution.

### Recursive Blocked Algorithms, Data Structures, and High-Performance Software for Solving Linear Systems and Matrix Equations

- Computer Science
- 2003

This thesis deals with the development of efficient and reliable algorithms and library software for factorizing matrices and solving matrix equations on high-performance computer systems. The arch…

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