4 edition of **impact of vector and parallel architectures on the Gaussian elimination algorithm** found in the catalog.

- 29 Want to read
- 19 Currently reading

Published
**1990**
by Manchester University Press, Wiley in Manchester, UK, New York
.

Written in English

- Computer architecture.,
- Vector processing (Computer science),
- Parallel processing (Electronic computers),
- Computer algorithms.,
- Gaussian processes.

**Edition Notes**

Includes bibliographical references (p. [183]-191) and index.

Statement | Yves Robert. |

Series | Algorithms and architectures for advanced scientific computing |

Classifications | |
---|---|

LC Classifications | QA76.9.A73 I55 1990 |

The Physical Object | |

Pagination | x, 194 p. : |

Number of Pages | 194 |

ID Numbers | |

Open Library | OL1886339M |

ISBN 10 | 0719033659, 0470217030 |

LC Control Number | 90047463 |

Gaussian elimination aims to transform a system of linear equations into an upper-triangular matrix in order to solve the unknowns and derive a solution. A pivot column is used to reduce the rows before it; then after the transformation, back-substitution is applied. Read The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm. SusanneBarger. Gauss elimination method using calculator (fx ES PLUS) IvoryDeborah YUNITA - REMEMBER ME THIS WAY (Jordan Hill) - Elimination 2 - Indonesian Idol

parallel solution of a nonsingular linear system by Gaussian elimination with partial pivoting on a distributed-memory MIMD machine. Because of the di culties and communication overheads associated with pivoting, it is tempting to try to avoid pivoting, but omission of pivoting in Gaussian elimination leads to numerical instability. Parallel Gaussian Elimination. CSE Term Project (Fall 96) Abstract. Gaussian Elimination is an algorithim used to solve a system of linear equations. The basic concept is to subract some scalar of an equation from another equation in order to eliminate an unkown. This is done repeatedly until the set of equations is trivial to solve.

In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.A tridiagonal system for n unknowns may be written as − + + + =, where = and. [⋱ ⋱ ⋱ −] [⋮] = [⋮].For such systems, the solution can be obtained. This paper considers elimination methods to solve dense linear systems, in particular a variant of Gaussian elimination due to Huard [13]. This variant reduces the system to an equivalent diagonal system just like Gauss-Jordan elimination, but does not require more floating-point operations than Gaussian elimination. To preserve stability, a pivoting strategy using column interchanges.

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Here is an in-depth examination of a single algorithm which ideally illustrates the basic concepts of vector and parallel processing: Gaussian elimination in three specific and active areas of parallel by: Buy The impact of vector and parallel architectures on the Gaussian elimination algorithm (Algorithms and architectures for advanced scientific computing) on FREE SHIPPING on.

The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm (Algorithms & Architectures for Advanced Scientific Computing) by Yves Robert Hardcover, Pages, Published ISBN / ISBN / Author: Yves Robert.

The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm by Yves Robert Hardcover, pages Published by John Wiley & Sons Publication date: February 1.

Book review: The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm b June ACM SIGARCH Computer Architecture News Siddhartha ChalterjeeAuthor: Rachid Saad. Robert, The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm (Manchester Univ.

Press, Manchester, ). [23] Y. Saad, Gaussian elimination on hypercubes, Res. Report YALEU/DCS/RR, [24]. [1] HighamN. J.,Gaussian elimination (Advanced Review), In: WIREs Computational Statistics,3(3), Google Scholar [2] Mayer J., A multilevel Crout ILU preconditioner with pivoting and row permutation, Numerical Linear Algebra with Applications,14(10), Google Scholar [3] Sibai F.

N., Performance modeling and analysis of parallel Gaussian elimination on multi-core. Introduction to Parallel Algorithms and Architectures: Arrays Trees Hypercubes provides an introduction to the expanding field of parallel algorithms and architectures.

This book focuses on parallel computation involving the most popular network architectures, namely, arrays, trees, hypercubes, and some closely related networks. Organized into three chapters, this book begins with an overview of the simplest architectures of arrays.

Gaussian Elimination such as the article by Howe and Bratcher [7] which compares cyclic and block mapping schemes. A good parallel algorithm for Gaussian Elimination is difficult, however, because of the inherent dependencies in the algorithm, plus the corresponding load balancing issues.

Both versions of the algorithm were run on an IBM RS. Gaussian Elimination The Gaussian elimination stage consists in sequential elimination of the unknowns in the equations of the linear equation system being solved.

At iteration i, 0≤ i. The impact of vector and parallel architectures on the Gaussian elimination algorithm. By Yves Robert.

Topics: [-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [] Publisher: Manchester University Press and John Wiley. Year: OAI identifier: oai:HAL:hal. Parallel Algorithm vs Parallel Formulation Parallel Formulation Refers to a parallelization of a serial algorithm.

Parallel Algorithm May represent an entirely different algorithm than the one used serially. We primarily focus on “Parallel Formulations” Our goal today is to primarily discuss how to develop such parallel formulations. The impact of vector and parallel architectures on the Gaussian elimination algorithm.

[Yves Robert] Part 2 Models and tools: task graph scheduling - task system for Gaussian elimation, bounds for parallel execution, an optimal schedule, with an arbitrary number of processors; analysis of distributed algorithms - data allocation strategies.

The Impact of Vector and Parallel Architectures on the Gaussian Elimination Algorithm, Halsted Press, New York. Introduction.

Vector and Parallel Architectures. Vector Multiprocessor Computing. Hypercube Computing. Systolic Computing. Task Graph Scheduling. Analysis of Distributed Algorithms. Design Methodologies. G.H. Golub and J.M. Ortega (). Gaussian elimination: Uses I Finding a basis for the span of given vectors.

This additionally gives us an algorithm for rank and therefore for testing linear dependence. I Solving a matrix equation,which is the same as expressing a given vector as a linear combination of other given vectors, which is the same as solving a system of. tiled algorithm for LU factorization 3 The PLASMA Software Library Parallel Linear Algebra Software for Multicore Architectures running an example MCS Lecture 21 Introduction to Supercomputing Jan Verschelde, 10 October Introduction to Supercomputing (MCS ) parallel Gaussian elimination L 10 October 1 / A Vector Implementation of Gaussian Elimination over GF(2): Exploring the Design-Space of Strassen’s Algorithm as a Case Study Enric Morancho Departament d’Arquitectura de Computadors Universitat Politècnica de Catalunya, BarcelonaTech Barcelona, Spain [email protected] 23rd Euromicro International Conference on.

Consider your inner loop. Every thread accesses A, and since k and j run from r to the end of the matrix, there is the potential for multiple threads to modify the same A[(ROWS + 1) * k + j] value.

You also potentially have some threads accessing A[(ROWS + 1) * r + j] while other threads are updating that value. One possible solution is to have each thread accumulate into individual result. The impact of vector and parallel architectures on the Gaussian Elimination Algorithm. Manchester University Press, Manchester University Press, Google Scholar.

Recent vector supercomputers provide vector memory access to “randomly” indexed vectors, whereas early vector supercomputers required contiguously or regularly indexed vectors.

This additional capability, known as “hardware gather/scatter,” can be used to great effect in general sparse Gaussian elimination. Communication Complexity of the Gaussian Elimination Algorithm on Multiprocessors Youcef Saad Research Center for Scientific Computation Yale University P.O.

BoxYale Station New Haven, Connecticut Submitted by J. Alan George ABSTRACT This paper proposes a few lower bounds for communication complexity of the Gaussian elimination algorithm on multiprocessors.Sequential Algorithm Gaussian Elimination Phase: 1.

For i = 1 to n, do a) If A[i,i] = 0 and A[m,i] = 0 for all m > i, conclude that A−1 does not exist and halt the algorithm. b) If A[i,i] = 0 and A[m, i] ≠ 0 for some smallest m > i, interchange rows i and m in the array A and in the array I.

c) Divide row i .CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): [2] Yves Robert. The impact of vector and parallel architectures on the Gaussian elimination algorithm.