Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem
نویسندگان
چکیده
منابع مشابه
Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem
It is well known that the solution of the equality constrained least squares (LSE) problem minBx=d ‖b−Ax‖2 is the limit of the solution of the unconstrained weighted least squares problem min x ∥∥ [ μd b ] − [ μB A ] x ∥∥ 2 as the weight μ tends to infinity, assuming that [B A ] has full rank. We derive a method for the LSE problem by applying Householder QR factorization with column pivoting t...
متن کاملThe Equality Constrained Indefinite Least Squares Problem : Theory and Algorithms ∗ †
We present theory and algorithms for the equality constrained indefinite least squares problem, which requires minimization of an indefinite quadratic form subject to a linear equality constraint. A generalized hyperbolic QR factorization is introduced and used in the derivation of perturbation bounds and to construct a numerical method. An alternative method is obtained by employing a generali...
متن کاملAccuracy and Stability of the Null Space Method for Solving the Equality Constrained Least Squares Problem
The null space method is a standard method for solving the linear least squares problem subject to equality constraints (the LSE problem). We show that three variants of the method, including one used in LAPACK that is based on the generalized QR factorization, are numerically stable. We derive two perturbation bounds for the LSE problem: one of standard form that is not attainable, and a bound...
متن کاملBackward Error Bounds for Constrained Least Squares Problems ∗
We derive an upper bound on the normwise backward error of an approximate solution to the equality constrained least squares problem minBx=d ‖b − Ax‖2. Instead of minimizing over the four perturbations to A, b, B and d, we fix those to B and d and minimize over the remaining two; we obtain an explicit solution of this simplified minimization problem. Our experiments show that backward error bou...
متن کاملAn Equality Constrained Least Squares Approach to the Structural Reanalysis
An efficient method for reanalysis of a damaged structures is presented. Perturbation analysis for the equality constrained least squares problem is adapted to handle structural reanalysis, and related theoretical and numerical results are presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1999
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479898335957