Accelerated dynamical approaches for finding the unique positive solution of $\mathcal {K}\mathcal {S}$-tensor equations

Autor: Maolin Che, Changxin Mo, Yimin Wei, Xuezhong Wang
Rok vydání: 2021
Předmět:
Zdroj: Numerical Algorithms. 88:1787-1810
ISSN: 1572-9265
1017-1398
DOI: 10.1007/s11075-021-01095-9
Popis: A new class of tensors called $\mathcal {K}\mathcal {S}$ -tensors, which is a subset of non-singular $\mathcal {P}$ -tensors and generalization of ${\mathscr{H}}^{+}$ -tensors, is proposed. It is proved that the system of $\mathcal {K}\mathcal {S}$ -tensor equations always has a unique positive solution for any positive right-hand side by proposing a positive increasing map. Two approaches based on dynamical system are presented to find the unique positive solution. The theoretical analysis results show that the convergence of the proposed models is guaranteed, and numerical examples further illustrate that the given models are feasible and effective in finding the positive solution of $\mathcal {K}\mathcal {S}$ -tensor equations.
Databáze: OpenAIRE
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