For the large sparse generalized absolute value equation (GAVE) , based on the shift splitting for the coefficient matrix of linear part, we establish a new modified Newton-type (NMN) iteration method. The convergence conditions of the NMN iteration method are discussed in depth. Furthermore, some specific sufficient convergence conditions are derived when the coefficient matrix is a symmetric positive definite matrix and an H_{+}-matrix. Both two numerical examples indicate that the NMN iteration method is an effective approach to solve the GAVE , especially when the coefficient matrix is indefinite.
For the large sparse generalized absolute value equations (GAVEs) , the shift splitting for the linear part's coefficient matrix is utilized to establish a new modified Newton-type (NMN) iteration method. The conditions for the convergence of the NMN iteration method are discussed in depth. Furthermore, certain sufficient convergence conditions are obtained when the coefficient matrix is a symmetric positive definite matrix or an H_{+}-matrix. According to both two numerical examples , the NMN iteration method is an effective approach to solve the GAVEs , especially when the coefficient matrix is indefinite.
R
equation (GAVE) , based on
equations (GAVEs) ,
R
coefficient matrix of linear part, we
linear part's coefficient matrix is utilized to
R
convergence conditions
conditions for the convergence
R
some specific
certain
R
derived
obtained
R
and
or
R
Both
According to both
R
indicate that
,
R
GAVE
GAVEs