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Parallel Triangular Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking [chapter]

Isak Jonsson, Bo Kågström
2001 Lecture Notes in Computer Science  
We present recursive blocked algorithms for solving triangular Sylvester-type matrix equations. Recursion leads to automatic blocking that is variable and \squarish".  ...  Uniprocessor and SMP parallel performance results are presented and compared with results from existing LAPACK routines for solving this type of matrix equations.  ...  In this contribution, we present new recursive blocked algorithms for solving triangular Sylvester-type matrix equations.  ... 
doi:10.1007/3-540-70734-4_10 fatcat:g6pdbwihxbbe5a3amazqrh7a7y

RECSY – A High Performance Library for Sylvester-Type Matrix Equations [chapter]

Isak Jonsson, Bo Kågström
2003 Lecture Notes in Computer Science  
RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability.  ...  The RECSY library comprises a set of Fortran 90 routines, which uses recursion and OpenMP for shared memory parallelism to solve eight different matrix equations, including continuous-time as well as discrete-time  ...  blocked algorithm for solving the triangular continuoustime Sylvester equation (SYCT)  ... 
doi:10.1007/978-3-540-45209-6_111 fatcat:5qi6k2ywqrhkbmsnaj7viymcyi

Combining Explicit and Recursive Blocking for Solving Triangular Sylvester-Type Matrix Equations on Distributed Memory Platforms [chapter]

Robert Granat, Isak Jonsson, Bo Kågström
2004 Lecture Notes in Computer Science  
Parallel ScaLAPACK-style hybrid algorithms for solving the triangular continuous-time Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel high-performance library  ...  The recursive blocking is automatic for solving subsystems of the global explicit blocked algorithm on the nodes.  ...  Acknowledgements This research was conducted using the resources of the High Performance Computing Center North (HPC2N  ... 
doi:10.1007/978-3-540-27866-5_97 fatcat:qnqd4po3dfd2rgglxd6hmimgum

Recursive blocked algorithms for solving triangular systems---Part II: two-sided and generalized Sylvester and Lyapunov matrix equations

Isak Jonsson, Bo Kågström
2002 ACM Transactions on Mathematical Software  
We continue our study of high-performance algorithms for solving triangular matrix equations.  ...  We present uniprocessor and SMP parallel performance results of recursive blocked algorithms and routines in the state-of-the-art SLICOT library.  ...  ACKNOWLEDGMENTS We thank Fred Gustavson and the colleagues in the Umeå HPC and Parallel Computing Research Group for stimulating and fruitful discussions.  ... 
doi:10.1145/592843.592846 fatcat:2wuper6xjbax5aw6zoypszmdvy

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

Erik Elmroth, Fred Gustavson, Isak Jonsson, Bo Kågström
2004 SIAM Review  
Novel recursive blocked algorithms offer new ways to compute factorizations such as Cholesky and QR and to solve matrix equations.  ...  matrix equations.  ...  This research was conducted using the resources of the High Performance Computing Center North (HPC2N), PDC-Parallelldatorcentrum at KTH, Stockholm, and UNI-C, Danish Technical University, Lyngby.  ... 
doi:10.1137/s0036144503428693 fatcat:7zmqj5eee5adxk56lbccrlyq3m

A framework for argument-based task synchronization with automatic detection of dependencies

Carlos H. González, Basilio B. Fraguela
2013 Parallel Computing  
In this paper we present a library-based approach that enables arbitrary patterns of parallelism with minimal effort for the user.  ...  needed among the parallel tasks.  ...  Finally, we thank the anonymous reviewers for their suggestions, which helped improve the paper.  ... 
doi:10.1016/j.parco.2013.04.012 fatcat:muzas3jetbecnjrmqh54sevy7i

Chapter 10: Algebraic Algorithms [article]

Ioannis Z. Emiris, Victor Y. Pan, Elias P. Tsigaridas
2013 arXiv   pre-print
Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical, for matrix computations and root-finding for polynomials and systems of polynomials equations.  ...  We cover part of these large subjects and include basic bibliography for further study.  ...  The Macaulay matrix simultaneously generalizes the Sylvester matrix and the coefficient matrix of a system of linear equations.  ... 
arXiv:1311.3731v1 fatcat:whtgwztbmbgqbl44s4e663oulu

Algebraic and Numerical Algorithms [chapter]

Ioannis Emiris, Victor Pan, Elias Tsigaridas
2009 Algorithms and Theory of Computation Handbook, Second Edition, Volume 1  
The Macaulay matrix simultaneously generalizes the Sylvester matrix and the coefficient matrix of a system of linear equations (67) .  ...  The Sylvester resultant can be used as a tool for eliminating several variables from a set of equations.  ... 
doi:10.1201/9781584888239-c17 fatcat:khegroceujdbpc3ukvlv6s3j4i

Knowledge-Based Automatic Generation of Linear Algebra Algorithms and Code [article]

Diego Fabregat-Traver
2014 arXiv   pre-print
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations.  ...  The development of efficient libraries for such equations, which lie at the heart of most software for scientific computing, is a complex process that requires expertise in a variety of areas, including  ...  Sylvester equation used as example throughout this chapter.  ... 
arXiv:1404.3406v1 fatcat:q7isxwrpjrgztis2743b2uq3re

MRRR-based Eigensolvers for Multi-core Processors and Supercomputers [article]

Matthias Petschow
2014 arXiv   pre-print
For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR or MR3 in short) - introduced in the late 1990s - is among the fastest methods.  ...  The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems  ...  test matrix types.  ... 
arXiv:1401.4950v1 fatcat:iiillrtypva3tmpv2d5mlmrkai