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Vietnam Journal of Mathematics 37:1 (2009) 91-96

An Algorithm for Solving the Nearest Point Problem in an Affine Subspace

Pham Canh Duong and Le Thanh Hue

Abstract.  We present a new algorithm for finding the projection of a vector into the intersection of a given set of hyperplanes in  Rⁿ. This algorithm is simple to implement and is shown to be more efficient than the well-known original conjugate gradient algorithm.

2000 Mathematics Subject Classification: 90C05, 90C59, 65K05, 65F10.

Keywords: Linear program, successive orthogonal projections algorithm, linear convergence, convex feasibility problem.

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013