Least Square Error Method Robustness of Computation: What is not usually considered and taught.

There are many practical applications based on the Least Square Error (LSE)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, ifdata span is large over several magnitudes or non-linear LSE is used, severenumerical instability can be expected. The presented contribution describes asimple method for large span of data LSE computation. It is especiallyconvenient if large span of data are to be processed, when the 'standard'pseudoinverse matrix is ill conditioned. It is actually based on a LSE solutionusing orthogonal basis vectors instead of orthonormal basis vectors. Thepresented approach has been used for a linear regression as well as forapproximation using radial basis functions.