Research On The Condition Numbers For Linear Least Squares Problem With Multiple Right-hand Sides

The condition number of a problem measures the effect on the solution of small changes in the data.In this paper,we establish some explicit expressions or easier computable upper bounds for relative normwise,mixed and componentwise condition numbers of the solution and residuals for linear least squares problem like min ?AXB-D?F whatever the matri-ces A and BT are have full column rank or they are rank deficient.We also derive the comparison of our upper bounds and the upper bounds given by[Chen et al.East Asian J.Applied Mathematics].In addition,we derived the condition numbers when A,B and D has some special structures.The obtained results are illustrated by corresponding numerical examples.