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lecture_08_SparseMatrices_pg06

# lecture_08_SparseMatrices_pg06 - P573 Scientific Computing...

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1 P573 Scientific Computing Lecture 8 - Sparse Matrices Peter Gottschling [email protected] www.osl.iu.edu/~pgottsch/courses/p573-06 2/27/06 P573 - Lecture 8: Sparse Matrices 2 Overview n Structured sparse matrices n Band matrices n Matrix vector product n Unstructured matrices n Matrix vector product n Other operations n Insertion 2/27/06 P573 - Lecture 8: Sparse Matrices 3 Tridiagonal Matrices n Diagonal and off-diagonals are only non-zero n For instance 1D-Poisson equation n Can be stored as vectors ! ! ! ! ! ! ! ! ! ! ! ! " # \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ % & () ( * * * * * * * * * * * * * + , - - - - - - - - - - - - - . / 0 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 0 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 2/27/06 P573 - Lecture 8: Sparse Matrices 4 Band Matrices n Extension of tridiagonal matrices n An (l, u)-m × n band matrices has n Only non-zeros in l diagonals below the main diagonal n Only non-zeros in u diagonals above the main diagonal n Formally: i " j > l # a ij = 0 j " i > u # a ij = 0

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2 2/27/06 P573 - Lecture 8: Sparse Matrices 5 Matrix of 2D-Poisson Equation n Off-diagonals with non-zeros only doesn’t need to stored n Instead of 0 diagonals we store offsets of non-zero off- diagonals n In example of 3x3 domain: {-3, -1, 0, 1, 3} = {o 0 , ..., o n } !
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lecture_08_SparseMatrices_pg06 - P573 Scientific Computing...

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