A compressed primal-dual method for generating bivariate cubic L1 splines

Authors:
Yong Wang;Shu-Cherng Fang;John E. Lavery
Affiliations:
SAS Institute Inc., Cary, NC 27513, USA;Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695-7906, USA and Departments of Mathematical Sciences and Industrial Engineering, Tsinghua Universit ...;Mathematics Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, we develop a compressed version of the primal-dual interior point method for generating bivariate cubic L"1 splines. Discretization of the underlying optimization model, which is a nonsmooth convex programming problem, leads to an overdetermined linear system that can be handled by interior point methods. Taking advantage of the special matrix structure of the cubic L"1 spline problem, we design a compressed primal-dual interior point algorithm. Computational experiments indicate that this compressed primal-dual method is robust and is much faster than the ordinary (uncompressed) primal-dual interior point algorithm.