• Amit Pathak
• Jaya Kushwah
• Suyash Dubey

Rational quintic splines offer a powerful blend of high-order continuity and flexible shape control, making them particularly valuable in interpolation, geometric design, and scientific computing. While polynomial quintic splines have been thoroughly studied in terms of error analysis and convergence, their rational counterparts have received less attention, especially with regard to explicit error bounds. This paper presents a comprehensive error bound analysis for a class of C2C^2C2-continuous rational quintic spline interpolants defined over a uniform mesh. The spline formulation includes rational basis functions governed by adjustable shape parameters, which enhance the spline’s ability to preserve features such as monotonicity and convexity. We derive explicit upper bounds for the interpolation error and its first and second derivatives, in terms of the mesh size hhh and the smoothness of the underlying function. These bounds extend classical results for polynomial splines and highlight the advantages of rational formulations when properly tuned. Numerical experiments confirm the theoretical convergence rates and demonstrate how the choice of rational parameters influences the accuracy of the spline.The results presented in this study establish a strong theoretical framework for using rational quintic splines in applications requiring both high accuracy and shape preservation, such as computer-aided design (CAD), data visualization, and numerical simulations.

Error Bound, Rational, Interpolation, quintic, cubic, shape preserving, parameter

"ERROR BOUND ANALYSIS OF RATIONAL QUINTIC SPLINE", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 6, page no.h466-h472, June-2025, Available :http://www.jetir.org/papers/JETIR2506760.pdf

"ERROR BOUND ANALYSIS OF RATIONAL QUINTIC SPLINE", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 6, page no. pph466-h472, June-2025, Available at : http://www.jetir.org/papers/JETIR2506760.pdf