Evaluating the Compressor performance using two dimensional Lagrange polynomial interpolation and Cubic approximation

  • 1 Department of Mathematical Engineering, Faculty of Mathematics and Physics Engineering, Polytechnic University of Tirana
  • 2 Department of Automation, Faculty of Electrical Engineering, Polytechnic University of Tirana, Albania


This paper talks about how we can use math to create better models based on actual compressor experiments. The goal? To bridge the gap between what we see happening in real life and what we can predict, ultimately helping us optimize HVAC systems for better performance.
Within these systems, parts like compressors, fans, and electrical components play crucial roles. Compressors, especially, are quite dynamic, especially in heat pump setups.
However, the problem is that manufacturers usually only give real-world data on how compressors perform, without detailed models for understanding how they work in different situations. Hopefully in this paper we will try to construct a detailed model in order to be able to evaluate a HVAC system without the necessity of real-world data. Also, we will evaluate two different mathematical models, two dimensional interpolation and approximation in order to see who perform better.



  1. Gentian Zavalaniand Michael Hecht. High-order numerical integration on regular embedded surfaces
  2. Saimir Tola1, Alfred Daci1,, Gentian Zavalani2, A Simulation of an Elastic Filament Using Kirchhoff Model
  3. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing (3rd ed.). Cambridge University Press.
  4. Atkinson, K. E. (1989). An Introduction to Numerical Analysis (2nd ed.). John Wiley & Sons.
  5. Phillips, G. M. (2003). Interpolation and Approximation by Polynomials. Springer.
  6. Chapra, S. C., & Canale, R. P. (2010). Numerical Methods for Engineers (6th ed.). McGraw-Hill Education.
  7. Iserles, A. (2009). A First Course in the Numerical Analysis of Differential Equations (2nd ed.). Cambridge University Press.

Article full text

Download PDF