The Core Error Problem in Variables for Statistical Least Squares with Interval Data
Stephen Ehidiamhen Uwamusi *
Department of Mathematical Sciences, Faculty of Natural Sciences, Kogi State University, Anyigba, Nigeria.
Andrew Esaborlupia Uwamusi
Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The paper discusses the core problem error in variables for statistical Least Squares which have noise in the data using polynomial fit of order three. Via Mobius transformation for complex disk in the sense of Petkovic, the exact inversion of a disk was described. Its pitfall was noted and Modified Certifylss relaxed refinement Cholesky decomposition in the sense of Rump comes in handy as a useful alternative for the solution of resulting interval linear system with guaranteed error bounds. The well known Oettli-Prager theorem was used as a measure of performance to the described method using the united solution set for the interval Hull as was described in the sense of Shary. It was discovered that the proposed technique performed as good with high yield of certainty in comparison with well known Oettli-Prager theorem. We also obtained results for traditional floating point arithmetic in the absence of noise in the data.
Keywords: Least squares, interval relaxed iterative refinement, mobius transformation, modified certifylss relaxed refinement cholesky decomposition, oetlli-prager theorem, ball arithmetic, united solution set.