Nekrasov Type Matrices and Upper Bounds for Their Inverses

In this paper, we consider ??Nekrasov matrices, a generalization of {P1, P2}?Nekrasov matrices obtained by introducing the set ? = {P1, P2, ..., Pm} of m simultaneous permutations of rows and columns of the given matrix. For point-wise and block ??Nekrasov matrices we give infinity norm bounds for the inverse. For ??Nekrasov B?matrices, obtained through a special rank one perturbation, we present main results on infinity norm bounds for the inverse and error bounds for linear complementarity problems. Numerical examples illustrate the benefits of new bounds.

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Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

Li¹,

Liu²,

Wang

2022

MATH

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<abstract><p>In this paper, a new proof that $ SDD_1 $ matrices is a subclass of $ H $-matrices is presented, and some properties of $ SDD_1 $ matrices are obtained. Based on the new proof, some upper bounds of the infinity norm of inverse of $ SDD_1 $ matrices and $ SDD $ matrices are given. Moreover, we show that these new bounds of $ SDD $ matrices are better than the well-known Varah bound for $ SDD $ matrices in some cases. In addition, some numerical examples are given to illustrate the corresponding results.</p></abstract>

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Nekrasov Type Matrices and Upper Bounds for Their Inverses

Cited by 3 publications

References 6 publications

Further Block Generalizations of Nekrasov Matrices

Further Block Generalizations of Nekrasov Matrices

On π−nekrasov matrices

Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

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