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

A New Modified Newton-Type Iteration Method for Solving Generalized Absolute Value Equations