Condition Numbers For Linear Least Squares Problem Involving Kronecker Product

Condition number is very important to matrix perturbation analysis,it describes the sensitivity of the solution to its input data of small perturbations.Many progress have been made on linear least squares problem.We shall study condition number of the least squares problem involving Kronecker product.Firstly,we consider the normwise,mixed and componentwise condition numbers of the least squares problem involving Kronecker product with multiple right-hand sides.The results extend the earlier condition numbers for the least squares problems with single right-hand side.Secondly,we study the condition number of the residual vector r that single righthand side least squares problem involving Kronecker product,we present the explicit expressions and upper bounds of the condition numbers.