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Principles Of Differential And Integral Equations

Several new criteria for identifying -tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of the obtained results are illustrated by numerical examples.

New practical criteria for ℋ-tensors and its application

Garcia-Esnaola and Pena (Numer. Algor. 67, 655–667, 2014) presented an error bound involving a parameter for linear complementarity problems of Nekrasov matrices. This bound is not effective in some cases because it tends to infinity when the involved parameter tends to zero. In this paper, the optimal value of this error bound is determined completely by using the monotonicity of functions of this parameter. Numerical examples are given to verify the corresponding results.

Note on error bounds for linear complementarity problems of Nekrasov matrices

In this paper, we introduce a new subclass of $ P $-matrices called Cvetkovic-Kostic-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. [ 24 ] for DZ-type-$ B $-matrices, and than that provided by M. Garcia-Esnaola and J.M. Pena [ 10 ] for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.

CKV-type $ B $-matrices and error bounds for linear complementarity problems

Strong $\mathcal{H}$
 -tensors play an important role in identifying the positive definiteness of even-order real symmetric tensors. In this paper, some new iterative criteria for identifying strong $\mathcal{H}$
 -tensors are obtained. These criteria only depend on the elements of the tensors, and it can be more effective to determine whether a given tensor is a strong $\mathcal{H}$
 -tensor or not by increasing the number of iterations. Some numerical results show the feasibility and effectiveness of the algorithm.

/pdf/new-iterative-criteria-for-strong-h-mathcal-h-tensors-and-an-2hwkmre6vb.pdf

New iterative criteria for strong H $\mathcal{H}$ -tensors and an application

A new error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix. This bound improves existing results. Finally, two numerical examples are also g...

New error bound for linear complementarity problems for B-matrices

Some new criteria for $\mathcal{H}$
 -tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. The advantages of the results obtained are illustrated by numerical examples.

/pdf/new-criteria-for-h-tensors-and-an-application-3c4x85grxo.pdf

New criteria for H-tensors and an application

Some new inequalities for the minimum eigenvalue of M-matrices are obtained These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices Finally, some examples are also given to show that the bounds are better than some previous results

/pdf/some-new-inequalities-for-the-minimum-eigenvalue-of-m-42a7bnaycd.pdf

Some new inequalities for the minimum eigenvalue of M-matrices

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Papers

New practical criteria for ℋ-tensors and its application

New error bound for linear complementarity problems for B-matrices

New criteria for H-tensors and an application

New criteria for H-tensors and an application

Some new inequalities for the minimum eigenvalue of M-matrices