  A shift splitting modified Newton-type (SSMN) iteration method is introduced
for solving large sparse generalized absolute value equations (GAVEs). The SSMN
method is established by replacing the regularized splitting of the coefficient
matrix of the linear part, which is employed in the modified Newton-type (MN)
iteration method, with the shift splitting of the matrix. The conditions for
the convergence of the proposed method are discussed in depth for the cases
when the coefficient matrix is a general matrix, a symmetric positive definite
matrix, and an $H_{+}$-matrix. Through two numerical examples, we find that the
SSMN and MN methods complement each other. The optimal performances of the two
methods depend on the definiteness of the coefficient matrix of the linear
part. The MN method is more efficient when the coefficient matrix is positive
definite, whereas the SSMN method has a better performance when the coefficient
matrix is indefinite.
