Nonsymmetric Algebraic Riccati Equations under the Tensor Product

Abstract

The nonsymmetric algebraic Riccati equation is proposed by using the tensor product. The existence of its minimal nonnegative solution is studied. The sufficient condition of the existence and the uniqueness of the minimal nonnegative solution is given by $\mathcal{M}$-tensor as well. The solution can be obtained by the fast Fourier transform which save computational cost of computing the required solution. Some numerical experiments are performed.

Keywords:

• Nonsymmetric algebraic Riccati equation
• T-$\mathcal{M}$-tensor
• the fast Fourier transform T-product

AMS subject classifications:

• 15A18
• 15A69
• 65F15
• 65F10
• 90C11

Notes

1 We cite another definition of the comparison matrix as follows which is slightly different from Definition 2.2.

Additional information

Funding

Y. Wei is supported by the National Natural Science Foundation of China under grant 12271108 and the Innovation Program of Shanghai Municipal Education Committee. The work of J. Yuan was partially supported by CNPq 301181/2017-9, Brazil, This reseqarch is supported by Shanghai Municipal Science and Technology Commission under grant 22WZ2501900.