## Lecture 28: Sparse matrix computations

### BibTeX

@MISC{Johnsson_lecture28:,

author = {Professor S. Lennart Johnsson},

title = {Lecture 28: Sparse matrix computations},

year = {}

}

### OpenURL

### Abstract

A sparse matrix is a matrix with relatively few nonzero elements. Often the number of nonzeroes amounts to much less than 1%. Sparse matrices arises in describing network problems in matrix form. The matrix typically captures the relationship between variables in different nodes of the network. The network may be given, as in various network flow problems for electric utilities, circuit simulation, oil or gas pipelines, or transportation problems with a fixed set of routes, as in urban transportation systems. The network may also arise due to the discretization of a continuum, as in the solution of partial differential equations. But, sparse matrices may also arise in other than network problems. For instance, a sparse matrix may be used to model the relationship between objects of some type in statistical analysis, or in molecular structures. In network problems, the number of nonzero elements in a row or column is directly related to the number of neighboring nodes. This number is often independent of the total size of the network. For sparse problems originating from partial differential equations, larger matrices are typically due to a refined discretization, or the treatment of bigger problems, neither of which have any direct influence on the number of neighbors of a node. The dependence remains local. The shape of the domain, or the nature of the solution are often having the strongest influence