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	Sparse matrix - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis a sparse matrix is a matrix populated primarily with zeros.
		When storing and manipulating sparse matrices on the computer, it is often necessary to modify the standard algorithms and take advantage of the sparse structure of the matrix.
		Sparse Matrix Algorithms Research at the University of Florida, containing the UF sparse matrix collection.
	en.wikipedia.org /wiki/Sparse_matrix (745 words)

	Sparse matrix: Facts and details from Encyclopedia Topic (via CobWeb/3.1 pl2.cs.utk.edu) (Site not responding. Last check: 2007-10-21)
		In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a ring-like algebraic structure....
		In the mathematical subfield of matrix theory the cuthill-mckee algorithm is an algorithm to reduce the bandwidth of sparse matrixsparse symmetric matrices....
		A sparse graph code is a code which is represented by a sparse graph....
	www.absoluteastronomy.com.cob-web.org:8888 /encyclopedia/s/sp/sparse_matrix.htm (1516 words)

	Sparse Matrix -- Recommendations and Resources (Site not responding. Last check: 2007-10-21)
		A sparse graph is a graph with a sparse adjacency matrix.
		Sparse mode multicast is one mode which multicast can use to construct a tree for sending packets to the multicast subscribers.
		Sparse mode is ideal for groups where a very low percentage of the nodes (and their routers) will subscribe to the multicast.
	www.becomingapediatrician.com /health/139/sparse-matrix.html (933 words)

	Latent semantic analysis - Wikipedia, the free encyclopedia (via CobWeb/3.1 pl2.cs.utk.edu) (Site not responding. Last check: 2007-10-21)
		LSA uses a term-document matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to documents and whose columns correspond to terms, typically stemmed words that appear in the documents.
		A typical example of the weighting of the elements of the matrix is tf-idf: the element of the matrix proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance.
		This matrix is common to standard semantic models as well (though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrix are not always used).
	en.wikipedia.org.cob-web.org:8888 /wiki/Latent_semantic_indexing (1269 words)

	Matrix Market: File Formats
		Matrix data is held in an 80-column, fixed-length format for portability.
		If there are no right-hand-side vectors, the matrix has a four-line header block followed by two or three data blocks containing, in order, the column (or element) start pointers, the row (or variable) indices, and the numerical values.
		M-file) is available which reads a matrix in coordinate text file format and creates a sparse matrix is available.
	math.nist.gov /MatrixMarket/formats.html (1705 words)

	Guide and Reference (Site not responding. Last check: 2007-10-21)
		A sparse matrix is a matrix having a relatively small number of nonzero elements.
		The storage mode used for square sparse matrices stored in compressed-diagonal storage mode has two variations, depending on whether the matrix is a general sparse matrix or a symmetric sparse matrix.
		The diagonal-out skyline storage mode used for sparse matrices has two variations, depending on whether the matrix is a general sparse matrix or a symmetric sparse matrix.
	csit1cwe.fsu.edu /extra_link/essl/essl148.html (2642 words)

	Fast and effective algorithms for graph partitioning and sparse-matrix ordering
		MD-based heuristics are local greedy heuristics that reorder the columns of a symmetric sparse matrix such that the column with the fewest nonzeros at a given stage of factorization is the next one to be eliminated at that stage.
		Partitioning the graph of a sparse matrix to minimize the edge cut and distributing different partitions to different processors minimizes the communication overhead in parallel sparse-matrix vector multiplication [12].
		Many implementations of sparse factorization switch to dense-matrix factorization at this stage because the cost of additional arithmetic operations is more than compensated for by the advantages of dense factorization, such as the absence of indirect addressing and better utilization of memory hierarchy.
	www.research.ibm.com /journal/rd/411/gupta.html (5952 words)

	Sparse Matrix Algorithms Research at the University of Florida
		Sparse Matrix Algorithms Research at the University of Florida
		UFsparse: All sparse matrix packages that I have authored or co-authored are available as a single tar or zip file here.
		Collaboration with Bill Hager modifying a sparse Cholesky factorization, graph partitioning, and optimization.
	www.cise.ufl.edu /research/sparse (272 words)

	Creating a sparse matrix
		The most common type of sparse matrix is a banded matrix, that is, a matrix with a few nonzero diagonals.
		In Matlab's indexing scheme, the nonzero diagonals of A are numbers -3, -1, 0, 1, and 3 (the main diagonal is number 0, the first subdiagonal is number -1, the first superdiagonal is number 1, and so forth).
		matrix containing the nonzero diagonals of A. Of course, the diagonals, regarded as column vectors, have different lengths; only the main diagonal has length 9.
	www.math.mtu.edu /~msgocken/intro/node18.html (396 words)

	Sparse Matrix Multiplication
		Sparse matrices, which are common in scientific applications, are matrices in which most elements are zero.
		A standard representation of sparse matrices in sequential languages is to use an array with one element per row each of which contains a linked-list of the nonzero values in that row along with their column number.
		In such an operation, the result is the dot-product of each sparse row of the matrix with the dense vector.
	www.cs.cmu.edu /~scandal/cacm/node9.html (414 words)

	Tim Davis: UF Sparse Matrix Collection : sparse matrices from a wide range of applications
		The UF Sparse Matrix Collection is a large set of sparse matrices from a wide range of problems.
		Sparse matrices from real applications are critical to the development of sparse matrix algorithms.
		If you would like the next generation of sparse matrix methods to work well on matrices from your problem domain, then please submit matrices to the collection, at: http://www.cise.ufl.edu/~web-gfs (user "davis").
	www.cise.ufl.edu /research/sparse/matrices (480 words)

	HB Files - The Harwell Boeing Sparse Matrix File Format
		If the matrix is read from the file into memory, it is common to use the same compressed column storage to represent the matrix in memory.
		If the matrix is sparse enough, then it is often much more efficient not to allocate space for the full m*n set of entries, but rather to keep track of the location and value of the nonzero entries.
		A indicates that the matrix is "assembled" (the typical case) while E indicates that the matrix is a finite element matrix that is going to be described as the "sum" of a set of smaller matrices.
	www.csit.fsu.edu /~burkardt/data/hb/hb.html (1251 words)

	SPARSEKIT - Sparse Matrix Utility Package
		For example, a matrix can be converted from the generalized diagonal format used by ELLPACK and ITPACK to the format used by the Harwell-Boeing Sparse Matrix Collection or into LINPACK banded format.
		CSPARSE is a set of C routines for direct sparse matrix operations.
		SPARSE is a built-in MATLAB function for defining sparse matrices.
	www.csit.fsu.edu /~burkardt/f_src/sparsekit/sparsekit.html (1614 words)

	Sparse Matrix Operations (Site not responding. Last check: 2007-10-21)
		Sparse Matrix Operations in NESL: Expressing sparse matrix operations is quite easy in NESL.
		Sparse Matrix Multiplication on Vector Multiprocessors: The NAS benchmark report includes timings of our Cray Y-MP/C90 implementation of the Conjugate Gradient benchmark.
		Our sparse matrix multiplication code for the Cray Y-MP family (written in Cray assembly language) is publicly available.
	www.cs.cmu.edu /~scandal/alg/sparse.html (353 words)

	Sparse Matrix Computation
		A Sparse Matrix is a matrix which has very few non-zero entries.
		A general trait of a unitary matrix is that it has a large number of zeros, although this is not always the case.
		It is highly inefficient in terms of both memory storage and network bandwidth to distribute a highly sparse matrix in normal rectangular format over the network.
	www.redbrick.dcu.ie /~hego/technicalmanual/node30.html (316 words)

	Sparse BLAS: A Baseline Implementation of the BLAS Standard
		Link to original NIST Sparse BLAS This is an implementation of a lower-level interface which was done before the BLAST Standard.
		where r is a scalar, x is a sparse vector, y is a dense vector, yx denotes the elements of y that are indexed by x.
		where A is a sparse matrix, T is an triangular sparse matrix, x and y are dense vectors, B and C are (usually tall and thin) dense matrices, and op(A) is either A, the transpose of A, or the Hermitian of A.
	math.nist.gov /spblas (555 words)

	Improving the memory-system performance of sparse-matrix vector multiplication
		Typically, accesses to the data structures that represent the sparse matrix A have no temporal locality¹ whatsoever, but they have good spatial locality (i.e., there is no data reuse, but accesses are in a stride-1 loop).
		The bandwidth of a sparse matrix is the maximum distance, in diagonals, between two nonzero elements of the matrix.
		Consequently, dense blocks in the matrix that was produced by the grid generator remained dense.
	www.research.ibm.com /journal/rd/416/toledo.html (7444 words)

	Sparsity Overview
		Sparse matrix-vector multiplication is an important computational kernel that arises in scientific simulations, data mining, image and signal processing, and other applications.
		Optimizing this algorithm is difficult, because the performance depends on the nonzero structure of the matrix as well as the characteristics of a given memory system.
		The first component is obtained through a search-like process of measuring the performance of a dense matrix in sparse format, blocked for a variety of sizes.
	www.cs.berkeley.edu /%7eyelick/sparsity (479 words)

	- الموسوعة العربية للكمبيوتر و الإنترنت[computers 4arab]
		ومن الصعب علينا تحديد ما إذا كانت المصفوفة عبارة عن Sparse Matrix أو لا..
		نقوم بإنشاء الـ Sparse Matrix ؛ نخزّن في البداية عدد الصفوف الكلي وعدد الأعمدة الكلي في كل من a[0].row و a[0].col..
		وسنتعرض لعملية تدوير المصفوفة المتناثرة أو مصفوفة الأصفار (Sparse Matrix Transpose) في الدرس القادم إن شاء الله..
	www.c4arab.com /showlesson.php?lesid=1036 (617 words)

	Sparse matrix (Site not responding. Last check: 2007-10-21)
		This matrix results from the linearisation of the discretisation of the Navier-Stokes type equations on a sphere.
		The matrix is described in a file that lists row, colomn and coefficient for all non zero entries.
		If the previous sample matrix was easy to solve, here is a slightly larger sample matrix with a size of 10362 This matrix is described in a file that lists row, colomn and coefficient for all non zero entries.
	www.atmos.ucla.edu /%7Enmolem/matrix (216 words)

	Sparse Matrix
		Assigns a matrix expression to the compressed matrix.
		Subtracts the matrix expression from the compressed matrix.
		Subtracts the matrix expression from the coordinate matrix.
	www.boost.org /libs/numeric/ublas/doc/matrix_sparse.htm (917 words)

	Sparse Matrix Ordering Example
		Graph theory was identified as a powerful tool for sparse matrix computation when Seymour Parter used undirected graphs to model symmetric Gaussian elimination more than 30 years ago [28].
		Therefore the nonzero pattern of a sparse matrix of a linear system can be modeled with a graph G(V,E), whose n vertices in V represent the n unknowns, and where there is an edge from vertex i to vertex j when A
		Thus, when a matrix has a symmetric nonzero pattern, the corresponding graph is undirected.
	www.boost.org /libs/graph/doc/sparse_matrix_ordering.html (1346 words)

	CS 340 Stack Project (Site not responding. Last check: 2007-10-21)
		Using the traditional definitions of mathematical matrices (matrix, matrix addition, and matrix multiplication), write a Java applet that allows the user to enter data into a single TextArea to create and perform operations on matrices using the data format described below.
		Your primary data structure must be a sparse matrix as described in class.
		name> is any String which begins with a capital letter and contains no spaces, such as "A" or "Matrix_1".
	homepage.mac.com /jimklayder/java/SparseMatrix/SparseMatrix.html (296 words)

	Citations: Compiler Support for Sparse Matrix Computations - Bik (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		However, the task of choosing a good representation for sparse matrices is a somewhat delicate one, and doing it right requires that careful attention be paid to the data flow of the algorithm, the structure of the non zeros in sparse matrices, and properties of the target architecture.
		Because the entries in a sparse storage scheme can usually only be generated efficiently along one particular direction, here it is also important to be able to change the access direction along arbitrary preferred directions.
		Because the entries in a sparse storage scheme can usually only be generated efficiently along one particular direction, here it is important to be able to change the access direction along arbitrary preferred directions before sparse storage schemes are selected by the compiler.
	citeseer.ist.psu.edu /context/380004/0 (1144 words)

	alphaWorks : Watson Sparse Matrix Package : Overview
		Watson Sparse Matrix Package (WSMP) is a collection of algorithms for efficiently solving large systems of linear equations whose coefficient matrices are sparse.
		A sparse matrix is one that has relatively few non-zero (or "interesting") entries.
		On a wide range of sparse linear systems and hardware platforms, WSMP has been shown to be significantly faster than other similar software.
	www.alphaworks.ibm.com /tech/wsmp (345 words)

	[No title]
		These bounds are based on the non-zero pattern in the matrix and the cost of basic memory operations, such as cache hits and misses.
		Many of the lower triangular factors arising in sparse LU factorization have a large, dense triangle in the lower right-hand corner of the matrix; this trailing triangle can account for as much as 90\% of the matrix non-zeros.
		To the sparse phase, we adapt the register blocking optimization, previously proposed for sparse matrix-vector multiply SpMxV in the Sparsity system, to the SpTS kernel; to the dense phase, we make judicious use of highly tuned BLAS routines by switching to a dense implementation (switch-to-dense optimization).
	bebop.cs.berkeley.edu /pubs/ABS-vuduc2002-sts-bounds.txt (1714 words)

	SOY/i - Sparse Operations with Yorick/IDL
		SOY/i (Sparse Operations with Yorick/IDL) originates from a collection of IDL/C routines that I originally put together for a specific purpose: efficient wavefront reconstruction in adaptive optics simulations.
		The sparse row-wise format (Chang et al., 1969; Gustavson, 1972) employed here is one of the most commonly used storage schemes for sparse matrices (also described in Press et al., 1992; Pissanetsky, 1984).
		A complication with sparse matrices is that you don't know from the start how large they need to be.
	homepage.mac.com /rflicker/soy.htm (1342 words)

	sparse matrix (Site not responding. Last check: 2007-10-21)
		It may be faster to represent the matrix compactly as a list of the non-zero indexes and associated entries, as a list of lists of entries (one list for each row), coordinate format (the values and their row/column positions), or by a point access method.
		A picture of another type of sparse matrix.
		Sparse matrix implementations, including the coordinate format, begin on page 85 (PDF page 97).
	www.nist.gov /dads/HTML/sparsematrix.html (195 words)

	SMC2001 (Site not responding. Last check: 2007-10-21)
		The course will focus on the solution of sparse linear systems of equations, and the lectures will be given by two distinguished researchers active in the field of sparse matrix computation:
		He has made a number of significant contributions in the fields of iterative solution of large, sparse systems of equations.
		Sparse matrices play an important role in modelling physical and technical problems.
	www2.imm.dtu.dk /~hbn/smc2001 (538 words)

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