1. What are the contributions in this paper?
In this paper, the authors extended the matrix computation language and environment Matlab to include sparse matrix storage and operations.
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Sparse matrices in matlab: design and implementation
TL;DR: The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations, and nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user.
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Abstract: The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.
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Figures
Table 2 E ect of permutations on Cholesky factorization. 
Fig. 7. Matrix S and its Cholesky factor after minimum degree reordering. 
Table 1 Operations with the 4096 by 4096 discrete Laplacian. 
Fig. 9. Solving Ax = b by block triangular back-substitution. 
Fig. 1. The Eppstein mesh as plotted by spy(A) and gplot(A,xy). 
Fig. 4. The structure of S and its Cholesky factor.
Citations
A fast diffeomorphic image registration algorithm
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The university of Florida sparse matrix collection
Timothy A. Davis,Yifan Hu +1 more
TL;DR: The University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications, is described and a new multilevel coarsening scheme is proposed to facilitate this task.
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The MATLAB ODE Suite
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From frequency to meaning: vector space models of semantics
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TL;DR: The goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs, and to provide pointers into the literature for those who are less familiar with the field.
Nonlinear Model Reduction via Discrete Empirical Interpolation
TL;DR: A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs).
References
Depth-First Search and Linear Graph Algorithms
TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.
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LINPACK Users' Guide
Jack Dongarra,Cleve B. Moler,J. R. Bunch,G. W. Stewart +3 more
- 01 Jan 1987
TL;DR: General matrices Band matrices positive definite matrices Positive definite band matrices Symmetric Indefinite Matrices Triangular matrices Tridiagonal matrices The Cholesky decomposition The QR decomposition up to and including the singular value decomposition is studied.
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ScaLAPACK Users' Guide
L. S. Blackford,Jae-Young Choi,A. Cleary,Eduardo D'Azevedo,James Demmel,Inderjit S. Dhillon,Jack Dongarra,Sven Hammarling,Greg Henry,A. Petitet,K. Stanley,David W. Walker,R. C. Whaley +12 more
- 01 Jan 1987
TL;DR: This book is very referred for you because it gives not only the experience but also lesson, it is about this book that will give wellness for all people from many societies.
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Matrix Eigensystem Routines - Eispack Guide
Brian T. Smith
- 01 Jan 1974
TL;DR: Eispack as discussed by the authors is an Eispack subroutine that uses handbook algol procedures to validate and validate EISPACKs and is used for EisPacks.
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