Sensitivity Analysis Of Sylvester Tensor Equation With Einstein Product

Sylvester-type equations have a huge amount of practical applications in image pro-cessing,statistics and probability,system and control theory,neural network,and eigenval-ue assignment problems.In addition,so far much effort has been devoted to the sensitivity analysis of 2nd-order tensor equations,i.e.matrix equations,but little has been done to that of general tensor equations.This paper focuses on the sensitivity of some tensor equations with respect to Einstein product.We investigate the backward error and perturbation bounds of the Sylvester tensor equation A*N X+X*N C=D.Also we discussed the norm bound on the sensitivity of the continue-time Laypunov tensor equation A*N X+X*N AT=G and discrete-time Laypunov tensor equation X-A*NX*N AT=Q.