Abstract
If the matrixA is not of full rank, there may be many solutions to the problem of minimizing ‖Ax−b‖ overx. Among such vectorsx, the unique one for which ‖x‖ is minimum is of importance in applications. This vector may be represented asx=A + b. In this paper, the functional equation technique of dynamic programming is used to find the shortest solution to the least-squares problem in a sequential fashion. The algorithm is illustrated with an example.
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References
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Our debt to the late Professor Richard Bellman is clear, and we wish to thank Professor Harriet Kagiwada for many stimulating conversations concerning least-squares problems over a long period of years.
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Kalaba, R., Xu, R. & Feng, W. Solving shortest length least-squares problems via dynamic programming. J Optim Theory Appl 85, 613–632 (1995). https://doi.org/10.1007/BF02193059
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DOI: https://doi.org/10.1007/BF02193059