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The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms.

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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. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.

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Structural representations of Schur complements in sparse matrices. Structural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed.

John R. Gilbert (Editor of Graph Theory and Sparse Matrix Computation)

Volume 21 , Issue 1. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Kincho H.

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Graph Theory and Sparse Matrix Computation

Please review our Terms and Conditions of Use and check box below to share full-text version of article. Get access to the full version of this article. View access options below. There are a number of functions that allow information concerning sparse matrices to be obtained. The most basic of these is issparse that identifies whether a particular Octave object is in fact a sparse matrix. Another very basic function is nnz that returns the number of nonzero entries there are in a sparse matrix, while the function nzmax returns the amount of storage allocated to the sparse matrix.

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Note that Octave tends to crop unused memory at the first opportunity for sparse objects. There are some cases of user created sparse objects where the value returned by nzmax will not be the same as nnz , but in general they will give the same result. The function spstats returns some basic statistics on the columns of a sparse matrix including the number of elements, the mean and the variance of each column.

See also: ismatrix.

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See also: nzmax , nonzeros , find. See also: find , nnz.

From Sparse Matrices to Graphs and Back Again

Thus, in general the value of nzmax will be the same as nnz except for some cases of user-created sparse objects. See also: nnz , spalloc , sparse. Called with two input arguments, if S is the data and j is the bin number for the data, compute the stats for each bin. In this case, bins can contain data values of zero, whereas with spstats S the zeros may disappear.