ON THE ERROR ESTIMATE FOR THE PROJECTION OF A POINT ONTO A LINEAR MANIFOLD

Suppose that the linear system AHx=b is consistent. The problem of finding the solution x to minA 1 2{norm of matrix}x-p{norm of matrix}22 is studied, where A∈Cn×m, b∈Cm, x,p∈Cn, and A, b, p are given. When A, b, and p are perturbed, an error bound for the solution x is obtained. Roundoff error bounds for the singular value decomposition method, the column pivoting method, and the rank revealing method are obtained. The results in this paper extend those of Arioli, Laratta, and Menchi to the case when A is not of full rank and either m≤n or m > n. © 1990.