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.
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.
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For the
A shift splitting modified Newton-type (SSMN) iteration method is introduced for solving
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, the shift splitting for the linear part's coefficient matrix is utilized to establish a new
. The SSMN method is established by replacing the regularized splitting of the coefficient matrix of the linear part, which is employed in the
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NMN
MN
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, with the shift splitting of the matrix
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NMN iteration
proposed
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. Furthermore, certain sufficient convergence conditions are obtained
for the cases
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general matrix, a
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or
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According to both
Through
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the NMN iteration method is an effective approach to solve the GAVEs, especially
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