Scientific and engineering research is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms on modern high-performance computers. Numerical linear algebra is an indispensable tool in such research and this paper attempts to collect and describe a selection of some of its more important parallel algorithms. The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers. A major emphasis is given here to certain computational primitives whose efficient execution on parallel and vector computers is essential in order to obtain high performance algorithms.

Parallel algorithms for dense linear algebra computations

In this review paper, we consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism. We briefly discuss the solution of dense linear systems, before studying the solution of sparse equations by direct and iterative methods. We consider preconditioning techniques for iterative solvers and discuss some of the present research issues in this field.

/pdf/developments-and-trends-in-the-parallel-solution-of-linear-2b6eeyoxa7.pdf

Developments and trends in the parallel solution of linear systems

Vector and parallel algorithms for finite-element analysis using the element-by-element (EBE) data structure are developed. The algorithms are based on the EBE approach in conjunction with gradient-type iterative solution. The essential idea is to exploit the independent dense local-element matrix-vector calculations and reconfigure them to take advantage of vector or parallel processing capabilities. The ideas also are well suited to finite-element adaptive refinement computations. Specific algorithmic details related to the implementations are given, together with results of speed-up performance studies conducted on the vector and parallel architectures. The basic vector and parallel versions of the matrix-vector product for the EBE scheme are very straightforward modifications of the EBE algorithm, requiring little coding change.

Element‐by‐element vector and parallel computations

Lösung linearer Gleichungssysteme auf Parallelrechnern

We investigate direct algorithms to solve linear banded systems of equations on MIMD multiprocessor computers with distributed memory We compare the coarse grain parallel algorithms with ordinary one processor Gaussian elimination The parallel algorithms behave satisfactory only if the ratio of bandwidth and matrix order is very small As a result of the high redundancy of the parallel algorithms e cencies are in general not high The theoretical considerations are complemented with numerical experiments performed on the Intel Paragon

/pdf/a-survey-of-direct-parallel-algorithms-for-banded-linear-27nh4wt63y.pdf

A survey of direct parallel algorithms for banded linear systems

The partition method of Wang for tridiagonal equations is generalized to the arbitrary band case. A stability criterion is given. The algorithm is compared to Gaussian elimination and cyclic reduction.

A parallel partition method for solving banded systems of linear equations

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

U Meier

Author Tools

Chat about Author

Papers

A parallel partition method for solving banded systems of linear equations