Tensor methods for large sparse systems of nonlinear equations
- Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
- Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
- Research Organization:
- Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 434848
- Report Number(s):
- MCS-P-473-1094; ON: DE97002612; CNN: AFOSR Gramt AGOSR-90-0109; AFOSR Grant F49620-94-1-0101; ARO Grant DAAL03-91-G-0151; ARO Grant DAAH04-94-G-0228; NSF Grant CCR-9101795
- Resource Relation:
- Other Information: PBD: [1996]
- Country of Publication:
- United States
- Language:
- English
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