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Sparse matrix computations with application to solve system of nonlinear equations

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Numerical linear algebra is an essential ingredient in algorithms for solving problems in optimization, nonlinear equations, and differential equations. Spanning diverse application areas, from economic planning to complex network analysis, modeling and solving problems arising in those areas share a common theme: numerical calculations on matrices that are sparse or structured or both. Linear algebraic calculations involving sparse matrices of order 109 are now routine. In this article, we give an overview of scientific calculations where effective utilization of properties such as sparsity, problem structure, etc. play a vital role and where the linear algebraic calculations are much more complex than their dense counterpart. This is partly because operation and storage involving known zeros must be avoided, and partly because the fact that modern computing hardware may not be amenable to the specialized techniques needed for sparse problems. We focus on sparse calculations arising in nonlinear equation solving using the Newton method. This article is categorized under: Applications of Computational Statistics > Computational Mathematics Data: Types and Structure > Categorical Data Algorithms and Computational Methods > Quadratic and Nonlinear Programming Algorithms and Computational Methods > Numerical Methods
Sparsity pattern.
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Effect of outer product updates on sparsity.
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Effect of permutation on fill‐in: original pattern (left), permuted pattern (right).
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Sparsity calculation.
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Compressed sparse row storage scheme.
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Coordinate storage scheme.
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Browse by Topic

Algorithms and Computational Methods > Numerical Methods
Algorithms and Computational Methods > Quadratic and Nonlinear Programming
Data: Types and Structure > Categorical Data
Applications of Computational Statistics > Computational Mathematics

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