Abstract
Non-negative least squares fitting is a basic block in many applications. Following the classical active-set method by Lawson and Hanson (Solving least squares problems, Prentice-Hall, 1974), much research has been directed toward improving that algorithm. In this paper we present a new method that produces an initial setting for this classical algorithm. This initialization method exploits the relationship between projection based methods and the active set methods. Two quantitative measurements are introduced to evaluate the quality of initial settings for active set method. Experimental results indicate that the proposed initialization provides a good jump-start for the active set method leading to a reduction of the number of iterations of active set methods.
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Acknowledgements
The work is supported by National High-Tech Research and Development Plan of China under Grant No. 2010AA012302, and National Basic Research Program of China (973) under Grant No.2006CB605102. The authors would like to thank Professor Ahmed Sameh at Purdue University for the helpful discussion and support from the beginning of this study. Thanks also go to Professor Stratis Gallopoulos at University of Patras for his comments and pointers to helpful information during the study of the method and the writing of the article. The authors would also like to thank Professor Guangwen Yang and Wei Xue for providing a great supportive environment for this study.
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Wang, M., Wang, X. (2012). A Jump-Start of Non-negative Least Squares Solvers. In: Berry, M., et al. High-Performance Scientific Computing. Springer, London. https://doi.org/10.1007/978-1-4471-2437-5_15
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DOI: https://doi.org/10.1007/978-1-4471-2437-5_15
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