Backward error bounds for constrained least squares problems

We derive an upper hound on the normwise backward error of an approximate solution to the equality constrained least squares problem, min(beta x,= d) //b - Ax//(2). Instead of minimizing over the four perturbations tu A, b, B and d, He fix those to B and d and minimize over the remaining two; rye obtain an explicit sc,solution of this simplified minimization problem. Our experiments show that ,backward error bounds of practical use are obtained when B and d are chosen as the ol,optimal normwise relative backward perturbations to the constraint system, and we find that when the bounds are weak they can be improved by direct search optimization. We also, derive upper and lower backward error bounds for the problem of least squares minimization over a sphere: min(//x//2 less than or equal to alpha) //b - Ax//(2) AMS subject classification: 65F20.