Abstract
We consider the least squares problem with a quadratic equality constraint (LSQE), i.e., minimizing |Ax-b|2 subject to $\|x\|_2=\alpha$, without the assumption $\|A^\dagger b\|_2>\alpha$ which is commonly imposed in the literature. Structure and perturbation analysis are given to demonstrate the sensitivity of the LSQE problem. We present a projection method combined with correction techniques (PMCT) for solving numerically the LSQE problem when the LSQE problem is ill-conditioned. We also give a detailed convergence analysis of our algorithms to illustrate the convergence behavior. Our algorithms have some obvious advantages over Newton's method and variants. Numerical experiments indicate that PMCT is much more efficient than Newton's methods when the LSQE problem is ill-conditioned; PMCT has a 90% success rate in terms of convergence, while commonly used Newton-type iterations almost always fail.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
