Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

/pdf/iterative-methods-for-sparse-linear-systems-34ozhpwq89.pdf

Iterative Methods for Sparse Linear Systems

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, 1993, 445--452; Hendrickson and Leland, A Multilevel Algorithm for Partitioning Graphs, Tech. report SAND 93-1301, Sandia National Laboratories, Albuquerque, NM, 1993]. From the early work it was clear that multilevel techniques held great promise; however, it was not known if they can be made to consistently produce high quality partitions for graphs arising in a wide range of application domains. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In particular, we present a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of the size of the final partition obtained after multilevel refinement. We also present a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening. We test our scheme on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that our scheme produces partitions that are consistently better than those produced by spectral partitioning schemes in substantially smaller time. Also, when our scheme is used to compute fill-reducing orderings for sparse matrices, it produces orderings that have substantially smaller fill than the widely used multiple minimum degree algorithm.

/pdf/a-fast-and-high-quality-multilevel-scheme-for-partitioning-2i240yved4.pdf

A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs

物件導向軟體之架構(Object-Oriented Software Construction)探討

This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than restricting attention to traditional nonlinear least squares.

/pdf/bundle-adjustment-a-modern-synthesis-449tfs1h4g.pdf

Bundle Adjustment - A Modern Synthesis

When reality is modelled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix; however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. They examine graph theory as it connects to linear algebra, parallel computing, data structures, geometry and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations; graph models of algorithms on nonsymmetric matrices; and parallel sparse matrix algorithms.

Graph theory and sparse matrix computation

This article deals with the problem of factoring a large sparse positive definite matrix on a multiprocessor system. The processors are assumed to have substantial local memory but no globally shared memory. They communicate among themselves and with a host processor through message passing. Our primary interest is in designing an algorithm which exploits parallelism, rather than in exploiting features of the underlying topology of the hardware. However, part of our study is aimed at determining, for certain sparse matrix problems, whether hardware based on the binary hypercube topology adequately supports the communication requirements for such problems. Numerical results from experiments conducted on a hypercube multiprocessor are included.

Sparse Cholesky factorization on a local-memory multiprocessor

Many algorithms for finding orderings for sparse symmetr ic matrices operate on the corresponding undirected graph. These algorithms often require one or more \"start ing nodes,\" and for some algorithms experience suggests tha t nodes which are at maximum or nearly maximum distance apar t are good candidates [4, 611]. In a recent paper, Gibbs et al. [8] provide a novel heuristic algorithm for finding such nodes. Our objective in this paper is to provide a well-structured flexible implementat ion of this algori thm which includes some .modifications tha t appear to improve its performance. We include some experiments demonstra t ing the effect of various modifications to the original algorithm. We now give some formal definitions and a precise s ta tement of the problem. Let G ffi (X, E) be an undirected graph with the set X of nodes and the set E of undirected edges represented as unordered pairs of nodes. A path of length k is an ordered set of distinct nodes (Xo, x l , . . . , Xk) where {x,-1, x,) E E for 1 _< i _ k. A graph is connected if for each pair of distinct nodes there is a path joining them. Throughou t this paper, graphs are assumed to be connected unless we state otherwise. Consider a connected graph G. The distance d(x, y) between two nodes x and y in G is defined to be the length of a shortest pa th connecting them. Following Berge [2], we define the eccentricity of a node x to be the quant i ty l(x) ffi max{d(x, y) [ y E X}.

An Implementation of a Pseudoperipheral Node Finder

This paper presents a column-oriented distributed algorithm for factoring a large sparse symmetric positive definite matrix on a local-memory parallel processor. Processors cooperate in computing each column of the Cholesky factor by calculating independent updates to the corresponding column of the original matrix. These updates are sent in a fan-in manner to the processor assigned to the column, which then completes the computation. Experimental results on an Intel iPSC/2 hypercube demonstrate that the method is effective and achieves good speedups.

A Fan-In Algorithm for Distributed Sparse Numerical Factorization

Parallel Cholesky factorization on a shared-memory multiprocessor☆

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.

Joseph W. H. Liu

Author Tools

Chat about Author