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

### Vaclav Skala

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 537–541 (2017)

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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