Abstract
We present a modified damped Newton method for solving large sparse linear complementarity problems, which adopts a new strategy for determining the stepsize at each Newton iteration. The global convergence of the new method is proved when the system matrix is a nondegenerate matrix. We then apply the matrix splitting technique to this new method, deriving an inexact splitting method for the linear complementarity problems. The global convergence of the resulting inexact splitting method is proved, too. Numerical results show that the new methods are feasible and effective for solving the large sparse linear complementarity problems.
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The research of this author is supported by The National Basic Research Program (No. 2005CB321702), The China NNSF National Outstanding Young Scientist Foundation (No. 10525102) and The National Natural Science Foundation (No. 10471146), P.R. China.
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Bai, ZZ., Dong, JL. A modified damped Newton method for linear complementarity problems. Numer Algor 42, 207–228 (2006). https://doi.org/10.1007/s11075-006-9028-4
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DOI: https://doi.org/10.1007/s11075-006-9028-4
Keywords
- linear complementarity problems
- damped Newton method
- inexact splitting method
- nondegenerate matrix
- \(H\)-matrix