In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matri...In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matrix absolute value equations(AVEs),the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity(or multilinearity)of the problem under consideration.Therefore,we first study the solutions existence of some classes of the TAVEs with the help of degree theory,in addition to showing,by fixed point theory,that the system of the TAVEs has at least one solution under some checkable conditions.Then,we give a bound of solutions of the TAVEs for some special cases.To find a solution to the TAVEs,we employ the generalized Newton method and report some preliminary results.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11571087 and 11771113)Natural Science Foundation of Zhejiang Province(Grant No.LY17A010028)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716 and 15300717)。
文摘In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matrix absolute value equations(AVEs),the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity(or multilinearity)of the problem under consideration.Therefore,we first study the solutions existence of some classes of the TAVEs with the help of degree theory,in addition to showing,by fixed point theory,that the system of the TAVEs has at least one solution under some checkable conditions.Then,we give a bound of solutions of the TAVEs for some special cases.To find a solution to the TAVEs,we employ the generalized Newton method and report some preliminary results.
