A reduced Newton method for constrained linear least-squares problems

Authors:
Benedetta Morini;Margherita Porcelli;Raymond H. Chan
Affiliations:
Dipartimento di Energetica "S. Stecco", Universití di Firenze, via C. Lombroso 6/17, 50134 Firenze, Italie;Dipartimento di Matematica "Ulisse Dini", Universití di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italie;Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.