Error analysis of algorithms for computing the projection of a point onto a linear manifold

M. Arioli, A. Laratta
1986 Linear Algebra and its Applications  
The accumulation of rounding errors in methods used to compute the projection of a point onto a linear manifold is studied. The methods are based on modified Gram-Schmidt, Householder, and Givens orthogonal factorizations. at the least distance from an assigned point p, i.e., the solution to the problem where the n x m real matrix A and the real m-vector b are known, and the n-vector x is unknown. In this paper, the Euclidean norm for the vectors and the corresponding induced norm for the
more » ... es are denoted by 11. )I, and the Frobenius norm by 11. I I F. The system (1.1) is assumed consistent even if the rank of A is not full. In any case, a linear dependence test and a consistency test of the system (1.1) are both useful in solving (1.2). For the case p = 0 Huang gives in [l] a method, based on the modified Gram-Schmidt decomposition of the matrix A, which includes these two tests. LINEAR ALGEBRA AND ITS APPLICATIONS 82:1-26 (1986) 1 0
doi:10.1016/0024-3795(86)90141-2 fatcat:f4d3bue6bbgnhnpwhudh4lse3q