The Core Error Problem in Variables for Statistical Least Squares with Interval Data

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.