Structured Condition Number For Least Squares Problems With Parameterized Quasiseparable Coefficient Matrices

In this thesis,we are concerned with the structured perturbation analysis for linear least squares problem(LS)with a parameterized coefficient matrix.Especially,we introduce the structured condition numbers for LS with the {1;1}-quasiseparable coefficient matrix with respect to the quasiseparable and the Givens-vector via tangent representations.The corresponding explicit expressions for structured condition numbers are obtained.Furthermore,the comparisons of these two structured condition numbers,and their relationships with respect to unstructured condition number are investigated Numerical experiments show that there are situations in which the structured condition numbers can be much smaller than the unstructured counterparts.