Sparse matrix computations with application to solve system of nonlinear equations
Version of Record online: 8 AUG 2013
© 2013 Wiley Periodicals, Inc.
Wiley Interdisciplinary Reviews: Computational Statistics
Volume 5, Issue 5, pages 372–386, September/October 2013
How to Cite
Hossain, S. and Steihaug, T. (2013), Sparse matrix computations with application to solve system of nonlinear equations. WIREs Comp Stat, 5: 372–386. doi: 10.1002/wics.1269
- Issue online: 22 AUG 2013
- Version of Record online: 8 AUG 2013
- Natural Sciences and Engineering Research Council of Canada
- Research Council of Norway
- Newton's method;
- sparse linear algebra;
- sparse matrix storage;
- Jacobian matrix
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.
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Conflict of interest: The authors have declared no conflicts of interest for this article.