Solving Discrete-Time Lyapunov Equations for the Cholesky Factor on a Shared Memory Multiprocessor
نویسندگان
چکیده
In this paper we study the parallel solution of the discrete time Lyapunov equation Two parallel ne and medium grain algorithms for solving dense and large order equa tions A X A X B B on a shared memory multiprocessor are presented They are based on Hammarling s method and directly obtain the Cholesky factor of the solution The parallel algorithms work following an antidiagonal wavefront In order to improve the performance column block oriented and wrap around algorithms are used Finally combined ne and medium grain parallel algorithms are presented
منابع مشابه
Parallel Cyclic Wavefront Algorithms for Solving Semidefinite Lyapunov Equations
In this paper we describe new parallel cyclic wavefront algo rithms for solving the semide nite discrete time Lyapunov equation for the Cholesky factor using Hammarling s method by the message passing para digm These algorithms are based on previous cyclic and modi ed cyclic algorithms designed for the parallel solution of triangular linear systems The experimental results obtained on an SGI Po...
متن کاملParallel ICCG on a Hierarchical Memory Multiprocessor- Addressing the Triangular Solve Bottleneck bY
The incomplete Cholesky conjugate gradient (ICCG) algorithm is a commonly used iterative method for solving large sparse systems of equations. In this paper, we study the parallel solution of sparse triangular systems of equations, the most difficult aspect of implementing the ICCG method on a multiprocessor. We focus on shared-memory multiprocessor architectures with deep memory hierarchies. O...
متن کاملAddress for Correspondence
Solving a system of linear equations i s a key problem in engineering and science. Matrix factorization is a key component of many methods used to solve such equations. However, the factorization process is very time consuming, so these problems have often been targeted for parallel machines rather than sequential ones. Nevertheless, commercially available supercomputers are expensive and only ...
متن کاملParallel ICCG on a hierarchical memory multiprocessor - Addressing the triangular solve bottleneck
The incomplete Cholesky conjugate gradient (ICCG) algorithm is a commonly used iterative method for solving large sparse systems of equations. In this paper, we study the parallel solution of sparse triangular systems of equations, the most difficult aspect of implementing the ICCG method on a multiprocessor. We focus on shared-memory multiprocessor architectures with deep memory hierarchies. O...
متن کاملRECSY - A High Performance Library for Sylvester-Type Matrix Equations
RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability. In order to achieve these goals, RECSY is based on novel recursive blocked algorithms, which call high-performance kernels for solving small-sized leaf problems of the recursion tree. In contrast to explicit standard blocking techniques, our recursive approach leads to an au...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Parallel Processing Letters
دوره 6 شماره
صفحات -
تاریخ انتشار 1996