Determining the Continuity of Some Polynomials Using Spline Functions
Akobi, Emmanuel Ogar *
Department of Mathematics and Statistics, University of Port Harcourt, Rivers State, 500001, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study provides an empirical and theoretical exploration of spline functions, focusing on their application in constructing the continuity of polynomials at breakpoints, commonly referred to as knots. The research outlines the mathematical foundation of spline functions and demonstrates their practical utility through illustrative example. Using blood pressure data from patients, a polynomial continuity model of order four was developed to address discontinuities at specified breakpoints. The model effectively ensures smooth transitions between polynomial segments, demonstrating its applicability in real-world scenarios. Additionally, the constructed continuity model shows potential for use in interpolation tasks, offering a robust framework for analysing and modeling data characterized by abrupt changes. This work highlights the versatility and effectiveness of spline functions in maintaining polynomial continuity and enhancing data interpolation methodologies.
Keywords: Polynomials, spline functions, theoretical exploration, mathematical foundation