Comparison of Lagrange and Newton interpolation formulas in concrete examples

Abstract

Annotation: This article studies the problem of algebraic interpolation, with particular attention to the theoretical foundations and practical application of Lagrange and Newton interpolation formulas. The concept of interpolation, interpolation nodes, and interpolating polynomials is discussed. The construction of the Lagrange interpolation polynomial using fundamental polynomials and its main drawbacks are analyzed. In addition, Newton’s interpolation formula based on divided differences is derived, and its computational advantages are highlighted. A numerical example is presented to construct and compare Lagrange and Newton interpolation polynomials. The obtained results demonstrate that both methods produce the same interpolation polynomial and are theoretically equivalent. The findings of the study are useful for selecting appropriate interpolation methods in numerical and computational mathematics problems.