Parallel Gauss-Jordan elimination for the solution of dense linear systems
نویسنده
چکیده
Any factorization/back substitution scheme for the solution of linear systems consists of two phases which are different in nature, and hence may be inefficient for parallel implementation on a single computational network. The Gauss-Jordan elimination scheme unifies the nature of the two phases of the solution process and thus seems to be more suitable for parallel architectures, especially if reconfiguration of the communication pattern is not permitted. In this communication, a computational network for the Gauss-Jordan algorithm is presented. This network compares favorably with optimal implementations of the Gauss elimina-tion/back substitution algorithm.
منابع مشابه
Stability of Gauss-Huard Elimination for Solving Linear Systems
This paper considers elimination methods to solve dense linear systems, in particular a variant due to Huard of Gaussian elimination [13]. This variant reduces the system to an equivalent diagonal system just as GaussJordan elimination, but does not require more floating-point operations than Gaussian elimination. Huard's method may be advantageous for use in computers with hierarchical memory,...
متن کاملMeasuring the Overhead of Intel C++ CnC over TBB for Gauss-Jordan Elimination
The most efficient parallel execution of dense liner algebra algorithms is to build and evaluate the task graph constrained only by the data dependencies between the tasks. Both Intel C++ Concurrent Collections (CnC) and Threading Building Blocks (TBB) libraries allow such task-based parallel programming. In this paper, we first analyze all the three types of data dependencies in the tiled in-p...
متن کاملSolving dense linear systems by Gauss-Huard's method on a distributed memory system
Introduction In this paper we present a modification of Gauss-Huard's method for solving dense linear systems that allows an efficient implementation on machines with a hierarchical memory structure. GaussHuard's method resembles Gauss-Jordan's method in the fact that it reduces the given system by elementary transformations to a diagonal system and it resembles regular Gaussian elimination in ...
متن کاملSystolic Gaussian Elimination over GF(p) with Partial Pivoting
We propose a systolic architecture for the triangularization via the Gauss elimination algorithm of large dense n x n matrices over GF@), where p is a prime number. The solution of large dense linear systems over GF(p) is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The proposed architecture implements the elimination with partial...
متن کاملDual Face Algorithm Using Gauss-jordan Elimination for Linear Programming
The dual face algorithm uses Cholesky factorization, as would be not very suitable for sparse computations. The purpose of this paper is to present a dual face algorithm using Gauss-Jordan elimination for solving bounded-variable LP problems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Parallel Computing
دوره 4 شماره
صفحات -
تاریخ انتشار 1987