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Polish Information Processing Society
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Annals of Computer Science and Information Systems, Volume 11

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

Least Square Method Robustness of Computations: What is not usually considered and taught

DOI: http://dx.doi.org/10.15439/2017F7

Citation: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 11, pages 537541 ()

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Abstract. There are many practical applications based on the Least Square Error (LSE) method approximation. It is based on a square error minimization ``on a vertical'' axis. The LSE method is simple and easy also for analytical purposes. However, if data span is large over several magnitudes or non-linear LSM is used, severe numerical instability can be expected. The presented contribution describes a simple method for large span of data LSE computation. It is especially convenient if large span of data are to be processed, when the ``standard'' pseudoinverse matrix is ill conditioned. It is actually based on a LSE solution using orthogonal basis vectors instead of orthonormal basis vectors. The presented approach has been used for a linear regression as well as for approximation using radial basis functions.


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