Dierent types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems are analyzed. The dierent algorithms which appeared in the literature are reviewed, and new ones are presented. Convergence properties of these algorithms are studied when the matrix in question is either monotone or an H-matrix. Relaxed versions of these algorithms are also studied. Computational experiments on a shared memory multiprocessor vector computer are presented.

Parallel, synchronous and asynchronous two-stage multisplitting methods

Parallel algorithms generated by multisplittings are considered. A parallel algorithm may be formed, first, by concurrently executing the iteration associated with each splitting, and second, by forming a weighted sum of these computations. However, it is not imperative that the weighting be done last. Convergence results are obtained for a variety of other weighting schemes. In particular, it is shown that preweighting is in some cases more desirable than the traditional postweighting. Furthermore, we indicate how one can use a symmetric weighting scheme to obtain a good multisplitting version of the SSOR preconditioner. These algorithms are illustrated by computations done on an Alliant $\text{FX} /8$ .

Multisplitting with different weighting schemes

In a previous paper, we have shown the very high power of asynchronism for parallel iterative algorithms in a global context of grid computing. In this article, we study the interest of coupling load balancing with asynchronism in such algorithms. After proposing a noncentralized version of dynamic load balancing which is best suited to asynchronism, we verify its efficiency by some experiments on a general partial differential equation (PDE) problem. Finally, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithm and discuss the choice of the residual as an efficient load estimator.

https://hal.archives-ouvertes.fr/hal-00096258/document

Dynamic load balancing and efficient load estimators for asynchronous iterative algorithms

A note on comparison theorems for splittings and multisplittings of Hermitian positive definite matrices

A multisplitting method for symmetric linear complementarity problems

Parallel iterative methods are studied, and the focus is on linear algebraic systems whose matrix is symmetric and positive definite. The set of unknowns may be viewed as a union of subsets of unknowns (possibly with overlap). The parallel iteration matrix is then formed by a weighted sum of iteration matrices that are associated with splittings of the matrix corresponding to the blocks. When the blocks are from a matrix in dissection form, it can be shown under suitable conditions that the parallel algorithm is convergent. When the multisplitting version of successive over-relaxation (SOR) is used, the SOR parameter is required to be less than $\omega _0 < 2.0$. Calculations done on the Alliant FX/8 multiprocessing/vector computer indicate speedups of nine to ten.

Multisplitting of a symmetric positive definite matrix

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.

R. E. White

Author Tools

Chat about Author

Papers

Multisplitting of a symmetric positive definite matrix