Structured Condition Number For Multi-right Hands Linear Systems With Parameterized Quasiseparable Coefficient Matrices

In this thesis,we are concerned with the structured perturbation analysis for multiright hands linear systems with parameterized coefficient matrix.Especially,we present the explicit expressions for structured condition numbers for multi-right hands linear systems with {1;1}-quasiseparable coefficient matrix in the quasiseparable and the Givensvector representations.In addition,the comparisons of these two condition numbers between themselves,and with respect to unstructured condition number will be investigated.Moreover,the effective structured condition number for multi-right hands linear systems with {1;1}-quasiseparable coefficient matrix is proposed,which can be computed with low operations.The relationships between the effective structured condition number and structured condition numbers with respect to the quasiseparable and the Givens-vector representations are also studied.Numerical experiments show that there are situations in which the effective structured condition number can be much smaller than the unstructured ones.