Normwise Condition Number And Small Sample Condition Estimations For The Linear Least Squares Problem With Quadric Inequality Constraints

In recent years,the general least squares with quadratic inequality constraints(GLSQI)problem has a wide application background.The numerical algorithms for GLSQI problems have emerged since 1980.The perturbation analysis of GLSQI problems is also an important research topic in the field of numerical algebra.In this thesis,we use Gratton’s results in the paper [23] to study the normwise expression of GLSQI problem and give the explicit expression.In addition,we prove that the derived explicit expressions are mathematically consistent with the corresponding results in [13].The above findings also can be applied to the standard least squares(LSQI)with quadratic inequality constraints problem.Since the GLSQI problem can be degenerated into the linear least squares problem(LS)under certain conditions,we show that the normwise,mixed and componentwise condition number expressions of the GLSQI problem can restore the previous results on normwise,mixed and componentwise condition number expressions of LS.Since Kronecker product is involved in the expressions of mixed and componentwise conditional numbers,it is difficult to calculate the above two kinds of condition numbers.We adopt the small sample statistical conditional number estimation to give the small sample statistical conditional number estimation of GLSQI problem.Numerical examples show that our estimates are reliable.