In this paper, we analyze the relationship between projected and (possibly accelerated) modulus-based matrix splitting methods for linear complementarity problems. In particular, first we show that some well-known projected splitting methods are equivalent, iteration by iteration, to some (accelerated) modulus-based matrix splitting methods with a specific choice of the parameter Ω. We then generalize this result to any Ω by formulating new classes of projected splitting methods and also provide a formal projection-based formulation for general (accelerated) modulus-based matrix splitting methods. Finally, we introduce and solve several test problems to evaluate also numerically the equivalence between the analyzed methods.

On the equivalence between some projected and modulus-based splitting methods for linear complementarity problems / Mezzadri, F.. - In: CALCOLO. - ISSN 0008-0624. - 56:4(2019), pp. 1-20. [10.1007/s10092-019-0337-0]

On the equivalence between some projected and modulus-based splitting methods for linear complementarity problems

Mezzadri F.
2019

Abstract

In this paper, we analyze the relationship between projected and (possibly accelerated) modulus-based matrix splitting methods for linear complementarity problems. In particular, first we show that some well-known projected splitting methods are equivalent, iteration by iteration, to some (accelerated) modulus-based matrix splitting methods with a specific choice of the parameter Ω. We then generalize this result to any Ω by formulating new classes of projected splitting methods and also provide a formal projection-based formulation for general (accelerated) modulus-based matrix splitting methods. Finally, we introduce and solve several test problems to evaluate also numerically the equivalence between the analyzed methods.
2019
56
4
1
20
On the equivalence between some projected and modulus-based splitting methods for linear complementarity problems / Mezzadri, F.. - In: CALCOLO. - ISSN 0008-0624. - 56:4(2019), pp. 1-20. [10.1007/s10092-019-0337-0]
Mezzadri, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1188540
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