Journal Article10.1109/PROC.1977.10514
A survey of sparse matrix research
Iain S. Duff
- 01 Apr 1977
- Vol. 65, Iss: 4, pp 500-535
275
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
read more
Abstract: This paper surveys the state of the art in sparse matrix research in January 1976. Much of the survey deals with the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms. In the symmetric case, relevant terms from graph theory are defined. Band systems and matrices arising from the discretization of partial differential equations are treated as separate cases. Preordering techniques are surveyed with particular emphasis on partitioning (to block triangular form) and tearing (to bordered block triangular form). Methods for solving the least squares problem and for sparse linear programming are also reviewed. The sparse eigenproblem is discussed with particular reference to some fairly recent iterative methods. There is a short discussion of general iterative techniques, and reference is made to good standard texts in this field. Design considerations when implementing sparse matrix algorithms are examined and finally comments are made concerning the availability of codes in this area.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Block-implicit calculation of steady turbulent recirculating flows
TL;DR: In this paper, a solution algorithm based on a fully-coupled solution of the Navier-Stokes equations is proposed to calculate steady multidimensional turbulent recirculating flows.
73
A numerically efficient finite-element formulation for the general waveguide problem without spurious modes
TL;DR: In this paper, a numerically efficient finite-element procedure without spurious modes is presented for the analysis of propagation characteristics in arbitrarily shaped metal waveguides loaded with linear materials of arbitrary complex tensor permittivity and permeability.
68
Electronically controlled multiphase sinusoidal oscillators using current amplifiers
TL;DR: In this paper, a novel current-mode multiphase oscillator topology is introduced by employing current amplifiers and only grounded capacitors, which has better performance in terms of the number of required active elements, the employment of passive resistors, and the ability for electronic adjustment of the oscillation frequency.
68
•Posted Content
DeepCABAC: A Universal Compression Algorithm for Deep Neural Networks
Simon Wiedemann,Heiner Kirchoffer,Stefan Matlage,Paul Haase,Arturo Marban,Talmaj Marinc,David Neumann,Tung Nguyen,Ahmed Osman,Detlev Marpe,Heiko Schwarz,Thomas Wiegand,Wojciech Samek +12 more
TL;DR: A universal compression algorithm for DNNs that is based on applying Context-based Adaptive Binary Arithmetic Coder (CABAC) to the DNN parameters, which applies a novel quantization scheme that minimizes a rate-distortion function while simultaneously taking the impact of quantization to theDNN performance into account.
Node and element resequencing using the Laplacian of a finite element graph: Part I—General concepts and algorithm
TL;DR: In this article, a spectral PEG resequencing (SFR) algorithm is proposed to reorder the nodes and/or elements of the associated finite element mesh, based on spectral properties of an FEG (G, G* or G˙).
61
References
•Book
Graph theory
Frank Harary
- 01 Jan 1969
TL;DR: This project focuses on Tutte’s work in cryptography, which enabled the British to read high-level German army messages and has been described as one of the greatest intellectual feats of the war.
18K
The Hungarian method for the assignment problem
TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
TL;DR: How heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching is described and an optimality property of a class of search strategies is demonstrated.
12.7K
•Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
- 01 Jan 1974
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
10.6K
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.