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A generalized Newton method for absolute value equations. (English) Zbl 1154.90599
Summary: A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax-|x|=b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy of 10 -6 in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 1,000×1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C53Methods of quasi-Newton type
Software:
Matlab
References:
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