Simple sparse matrices we have seen so far include diagonal matrices and tridiagonal matrices, but these are not the only ones.
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1 A matrix is sparse if most of its entries are zero. Simple sparse matrices we have seen so far include diagonal matrices and tridiagonal matrices, but these are not the only ones. In fact sparse matrices appear in many applications areas from structural analysis to fluid dynamics and from DNA sequencing to graph theory. Examples: Structural mechanics: load on a plane truss Directed graph for a network
2 A matrix is sparse if most of its entries are zero. Simple sparse matrices we have seen so far include diagonal matrices and tridiagonal matrices, but these are not the only ones. In fact sparse matrices appear in many applications areas from structural analysis to fluid dynamics and from DNA sequencing to graph theory. Examples: Pattern of non-zeros in the linear system for determining the force balance 0 Pattern of non-zeros in the adjacency matrix for the graph nz = nz = 1
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5 If a matrix has a high sparsity ratio and a small bandwidth then fast algorithms can typically be used to solve linear systems with these matrices. MATLAB has state-of-the-art libraries for computing with sparse matrices.
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